Límites.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color='crimson'> Clase del 14 de octubre </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt #biblioteca para graficar\n",
    "import numpy as np #numerical python - para hacer cuentas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definir la sucesión recursiva:\n",
    "    $$x_{n+1}=\\frac{1}{2}\\left(x_n+\\frac{a}{x_n}\\right)$$\n",
    "donde $a>0$ y $x_0$ es un número real cualquiera, que se elige por conveniencia como cercano a $\\sqrt{a}$. La idea es que:\n",
    "    $$\\lim_{n\\to\\infty} x_n = \\sqrt{a}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x0,a,n):\n",
    "    x=x0 \n",
    "    for i in range(n): \n",
    "        x=0.5*(x+a/x) \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=[f(1,2,i) for i in range(1,20)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.plot(X,'.',linewidth=5)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los números del arreglo X, que contiene $x_1,\\dots,x_{20}$, se acercan no solamente entre sí, sino también a la raíz de 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.5,\n",
       " 1.4166666666666665,\n",
       " 1.4142156862745097,\n",
       " 1.4142135623746899,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095,\n",
       " 1.414213562373095]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Otro ejemplo** La sucesión $a_n=\\frac{n}{n+1}$ converge a 1:\n",
    "    $$\\lim_{n\\to\\infty} a_n = 1$$\n",
    "lo que significa que, sin importar el \"error\" $\\epsilon>0$, habrá un momento $N\\in\\mathbb{N}$ en la sucesión a partir del cual los términos $a_{N+1},a_{N+2},\\dots$ (es decir, los términos $a_n$ para $n>N$) están a una distancia del 1 menor a $\\epsilon$:\n",
    "    $$\\left| a_n - 1 \\right|<\\epsilon \\;\\; \\forall n>N$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a_0=0.000,\t|a_0-1|=1.000\n",
      "a_1=0.500,\t|a_1-1|=0.500\n",
      "a_2=0.667,\t|a_2-1|=0.333\n",
      "a_3=0.750,\t|a_3-1|=0.250\n",
      "a_4=0.800,\t|a_4-1|=0.200\n",
      "a_5=0.833,\t|a_5-1|=0.167\n",
      "a_6=0.857,\t|a_6-1|=0.143\n",
      "a_7=0.875,\t|a_7-1|=0.125\n",
      "a_8=0.889,\t|a_8-1|=0.111\n",
      "a_9=0.900,\t|a_9-1|=0.100\n",
      "a_10=0.909,\t|a_10-1|=0.091\n",
      "a_11=0.917,\t|a_11-1|=0.083\n",
      "a_12=0.923,\t|a_12-1|=0.077\n",
      "a_13=0.929,\t|a_13-1|=0.071\n",
      "a_14=0.933,\t|a_14-1|=0.067\n",
      "a_15=0.938,\t|a_15-1|=0.062\n",
      "a_16=0.941,\t|a_16-1|=0.059\n",
      "a_17=0.944,\t|a_17-1|=0.056\n",
      "a_18=0.947,\t|a_18-1|=0.053\n",
      "a_19=0.950,\t|a_19-1|=0.050\n",
      "a_20=0.952,\t|a_20-1|=0.048\n",
      "a_21=0.955,\t|a_21-1|=0.045\n",
      "a_22=0.957,\t|a_22-1|=0.043\n",
      "a_23=0.958,\t|a_23-1|=0.042\n",
      "a_24=0.960,\t|a_24-1|=0.040\n",
      "a_25=0.962,\t|a_25-1|=0.038\n",
      "a_26=0.963,\t|a_26-1|=0.037\n",
      "a_27=0.964,\t|a_27-1|=0.036\n",
      "a_28=0.966,\t|a_28-1|=0.034\n",
      "a_29=0.967,\t|a_29-1|=0.033\n",
      "a_30=0.968,\t|a_30-1|=0.032\n",
      "a_31=0.969,\t|a_31-1|=0.031\n",
      "a_32=0.970,\t|a_32-1|=0.030\n",
      "a_33=0.971,\t|a_33-1|=0.029\n",
      "a_34=0.971,\t|a_34-1|=0.029\n",
      "a_35=0.972,\t|a_35-1|=0.028\n",
      "a_36=0.973,\t|a_36-1|=0.027\n",
      "a_37=0.974,\t|a_37-1|=0.026\n",
      "a_38=0.974,\t|a_38-1|=0.026\n",
      "a_39=0.975,\t|a_39-1|=0.025\n",
      "a_40=0.976,\t|a_40-1|=0.024\n",
      "a_41=0.976,\t|a_41-1|=0.024\n",
      "a_42=0.977,\t|a_42-1|=0.023\n",
      "a_43=0.977,\t|a_43-1|=0.023\n",
      "a_44=0.978,\t|a_44-1|=0.022\n",
      "a_45=0.978,\t|a_45-1|=0.022\n",
      "a_46=0.979,\t|a_46-1|=0.021\n",
      "a_47=0.979,\t|a_47-1|=0.021\n",
      "a_48=0.980,\t|a_48-1|=0.020\n",
      "a_49=0.980,\t|a_49-1|=0.020\n"
     ]
    }
   ],
   "source": [
    "for i in range(50):\n",
    "    k=i/(i+1)\n",
    "    print('a_{0}={1:.3f},\\t|a_{0}-1|={2:.3f}'.format(i,k,abs(1-k)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Conforme n crece, n/(n+1) se acerca a 1 (lo que equivale a decir que la distancia de $a_n$ al 1 tiende a ser más y más chica). Decimos entonces:_\n",
    "\\begin{equation}\n",
    "\\lim_{n\\to\\infty} \\frac{n}{n+1}=1\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color='crimson'> Clase del 15 de octubre </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Primero consideramos la sucesión de funciones: para cada $x\\in(0,1)$:\n",
    "   $$ f_{n}(x):=\\sum_{k=0}^n x^k\\equiv \\frac{1-x^{n+1}}{1-x} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observación 1** \n",
    "    $$\\lim_{n\\to\\infty} x^n=0$$ \n",
    "\n",
    "siempre y cuando $x\\in(0,1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x^1000=1.7478712517226947e-46\n",
      "x^1001=1.5730841265504254e-46\n",
      "x^1002=1.4157757138953828e-46\n",
      "x^1003=1.2741981425058445e-46\n",
      "x^1004=1.1467783282552602e-46\n",
      "x^1005=1.0321004954297341e-46\n",
      "x^1006=9.288904458867608e-47\n",
      "x^1007=8.360014012980847e-47\n",
      "x^1008=7.524012611682763e-47\n",
      "x^1009=6.771611350514486e-47\n",
      "x^1010=6.094450215463038e-47\n",
      "x^1011=5.485005193916734e-47\n",
      "x^1012=4.9365046745250605e-47\n",
      "x^1013=4.442854207072555e-47\n",
      "x^1014=3.9985687863652993e-47\n",
      "x^1015=3.59871190772877e-47\n",
      "x^1016=3.238840716955893e-47\n",
      "x^1017=2.914956645260304e-47\n",
      "x^1018=2.623460980734273e-47\n",
      "x^1019=2.361114882660846e-47\n",
      "x^1020=2.1250033943947614e-47\n",
      "x^1021=1.9125030549552855e-47\n",
      "x^1022=1.7212527494597569e-47\n",
      "x^1023=1.5491274745137813e-47\n",
      "x^1024=1.394214727062403e-47\n",
      "x^1025=1.2547932543561628e-47\n",
      "x^1026=1.1293139289205466e-47\n",
      "x^1027=1.016382536028492e-47\n",
      "x^1028=9.147442824256428e-48\n",
      "x^1029=8.232698541830785e-48\n",
      "x^1030=7.409428687647707e-48\n",
      "x^1031=6.668485818882936e-48\n",
      "x^1032=6.001637236994643e-48\n",
      "x^1033=5.401473513295179e-48\n",
      "x^1034=4.861326161965661e-48\n",
      "x^1035=4.3751935457690953e-48\n",
      "x^1036=3.9376741911921854e-48\n",
      "x^1037=3.543906772072967e-48\n",
      "x^1038=3.1895160948656705e-48\n",
      "x^1039=2.870564485379103e-48\n",
      "x^1040=2.583508036841193e-48\n",
      "x^1041=2.325157233157074e-48\n",
      "x^1042=2.0926415098413665e-48\n",
      "x^1043=1.88337735885723e-48\n",
      "x^1044=1.695039622971507e-48\n",
      "x^1045=1.5255356606743564e-48\n",
      "x^1046=1.3729820946069208e-48\n",
      "x^1047=1.2356838851462287e-48\n",
      "x^1048=1.1121154966316058e-48\n",
      "x^1049=1.0009039469684453e-48\n"
     ]
    }
   ],
   "source": [
    "def pot(x,n):\n",
    "    return x**n\n",
    "\n",
    "x=0.9 #En esta x vamos a examinar sus potencias sucesivas\n",
    "for i in range(1000,1050):\n",
    "    print('x^{0}={1}'.format(i,pot(x,i)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Un número positivo menor a 1 ($x\\in(0,1)$) elevado a potencias enteras crecientes, tiende a disminuir._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observación 2**\n",
    "        $$\\lim_{n\\to\\infty} f_n(x)=\\lim_{n\\to\\infty} \\sum_{k=0}^n x^k=\\lim_{n\\to\\infty} \\left( 1+x+x^2+\\cdots+x^n\\right)=\\frac{1}{1-x} \\;\\; \\forall x\\in(0,1) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Fijamos x y consideramos $n$ cada vez más grande. La idea es que $f_n(x)$ de x se acerca a $\\frac{1}{1-x}$ si $n$ es grande._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f_1000 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1001 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1002 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1003 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1004 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1005 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1006 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1007 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1008 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1009 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1010 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1011 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1012 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1013 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1014 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1015 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1016 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1017 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1018 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n",
      "f_1019 (x)=9.999999999999993,\t 1/(1-x)=10.000000000000002\n"
     ]
    }
   ],
   "source": [
    "def F(x,n): #Aquí defino las funciones f_n(x)\n",
    "    return sum([x**i for i in range(n+1)])\n",
    "\n",
    "def lim(x):\n",
    "    return 1/(1-x)\n",
    "\n",
    "x=0.9\n",
    "for i in range(1000,1020): \n",
    "    print('f_{} (x)={},\\t 1/(1-x)={}'.format(i,F(x,i),lim(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ver el proceso límite mediante sus gráficas**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "<img 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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "X=np.linspace(0,1,200,endpoint=False)\n",
    "for i in [1,2,5,10,100,1000]: #graficar f_1(x), f_2(x), ..., f_1000(x)\n",
    "    plt.plot(X,F(X,i),label='$f_{{{0}}}(x)$'.format(i))\n",
    "plt.plot(X,lim(X),'.',lw=2,c='blue',label='$1/(1-x)$') #graficar 1/(1-x)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Las funciones $f_{n}(x)$ se acercan más y más a $\\frac{1}{1-x}$ conforme $n\\in\\mathbb{N}$ crece. Esto se observa en las líneas continuas, que se acercan más y más al comportamiento de la función representada con puntos azules._"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}