mat301c-soln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "<big>Lab C: Finding Limits in Python</big><br>\n",
    "https://mybinder.org/v2/gh/anniebmcc/pycalclab/master?filepath=mat301c.ipynb <br>\n",
    "2020 Summer — Calculus 1<br>\n",
    "Dr Matthew H Sunderland<br>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C1. _RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magic word `%pylab` loads a bunch of useful functions (including `pi` and `sin`).  \n",
    "The option `inline` tells Jupyter to display any graphs we make on the page instead of in a popup."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C2. Example.\n",
    "Let's say we want to find $\\displaystyle \\lim_{\\textstyle x{\\to}\\pi/2} \\frac{\\sin x}x$.\n",
    "The first thing we try is plugging in.  \n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6366197723675814"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = pi/2\n",
    "sin(x)/x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C3. **DO EXERCISE.** Based on the result in C2, what is the value of the limit\n",
    "$\\displaystyle \\lim_{\\textstyle x{\\to}\\pi/2} \\frac{\\sin x}x$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# RECORD YOUR ANSWER: the limit is 0.6366197723675814"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C4. Example. Let's say we want to find $\\displaystyle \\lim_{\\textstyle x{\\to}0} \\frac{\\sin x}x$ instead.   \n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sunderland20a/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 0\n",
    "sin(x)/x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that plugging in doesn't work, because sin(0)/0 is undefined.  \n",
    "(Instead of \"undefined\", Python says \"nan,\" which means \"not a number.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the limit with a graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C5. When plugging in doesn't work, one thing we can try is graphing.  \n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed1379aa90>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vsujrRITZzgFYSp0qDXzllXqCz1/O8MHxvRZVHqOxtcPuUpSX0sBXXimvpI7w4EAmjYqyuxS3mZUahzGwrUxnzlSnRgNfeaWCsjpmjI0lyAdnyByIXrhVw+U/vy3KZ7R3drPjUINPz5/Tn9iIYDISdeZMdeo08JXXKaxooL3Tt2fIHMhsnTlTDYMGvvI6PSNsfX1Khf7MSo2jsrGNivpWu0tRXsiSwBeRxSKyW0SKROSeE2x3pYgYEcmxYr/KP+WX1JEUHcqY2DC7S3G7nk812qyjTsWwA19EAoHHgIuALGCJiGT1s1008ENg43D3qfxbzwyZImJ3KW43dXQMIYEBGvjqlFhxhj8fKDLGFBtj2oFXgMv62e7XwMOAfhZVp6y+uYPiqia/bL8HCAlyLNauUyWrU2FF4I8FSnvdL3M+dpyIZAOpxph/nuiFRORWEdkiIlsqKystKE35Gn+aIXMgs1Pj2F5eT6fOnKmGyOUXbUUkAPg98OOTbWuMedIYk2OMyUlKSnJ1acoLfT5DZqzdpdhmTlocLR1d7DlyzO5SlJexIvDLgdRe91Ocj/WIBqYDH4nIAWABsFIv3KpTkV9aR2ZSFNFhwXaXYhu9cKtOlRWBvxmYKCLjRSQEuBZY2fOkMabeGJNojBlnjBkHbAAuNcZssWDfyo8YY8gvrfPL7pi9pSVEEB8RTH5prd2lKC8z7MA3xnQCdwCrgULgNWPMDhH5lYhcOtzXV6pHWW0LNU3tft1+D46ZM2elxlFQqnPqqKGxZOUIY8wqYFWfxx4YYNtzrNin8j95fjhD5kBmp8bx8Z69HGvr9IsFYJQ1dKSt8hr5JXWEBgUwOTna7lJs9/nMmdqOrwZPA195jZ4ZMoP9aIbMgfTMnKnNOmoo9DdHeYWOrm4+K6/X5hyn+MgQxo2I0Au3akg08JVXKKxooK2z2++mRD6ROWnx5JbozJlq8DTwlVfIPeg4k81O8481bAdjTppj5szyuha7S1FeQgNfeYXckjqSY8IYExdudykeo+ePX67Oq6MGSQNfeYW80lrmaHPOF0xJjiYsOIC8Em3HV4Ojga88XmVjG6U1Ldqc00dQYAAzU+L0DF8Nmga+8ni5zjPY7HQ9w+8rOy2enYfqae3osrsU5QU08JXHyyupIzhQmDbGf2fIHEh2WhwdXYYdh7Q/vjo5DXzl8XJLaskaE0tYcKDdpXicOT0Xbg9qs446OQ185dE6urrZVlZHtl6w7VdSdCipCeHHm72UOhENfOXRdh9upLWj+/iZrPqy7LR48vTCrRoEDXzl0Y5fsNUz/AHNSY3jcEMrh3QAljoJDXzl0XIP1jIyOpSxOuBqQNnpPQOwtFlHnZgGvvJoeaV1zEmLQ0TsLsVjTR0d4xyApc066sQ08JXHqjrWxsHqZh1wdRLBgQHMHBunZ/jqpDTwlcfqOWPtabJQA5uTFseO8gbaOnUAlhqYBr7yWHkltQQFCDPG6oCrk5mTFk97Vzc7DjXYXYryYBr4ymM5BlzF6ICrQejpxdQzjbRS/dHAVx6ps6ubgtJ6bb8fpJExYYyNC9cLt+qENPCVR9p9pJGWji6dEnkIstPjdapkdUIa+Moj9Uz5q2f4g5edFseh+lYO17faXYryUBr4yiPlHawlMSqUlHgdcDVYxydS07N8NQBLAl9EFovIbhEpEpF7+nn+LhHZKSLbROR9EUm3Yr/Kd+WW1OqAqyHKGh1DaFCAXrhVAxp24ItIIPAYcBGQBSwRkaw+m+UBOcaYmcDfgEeGu1/lu2qa2jmgA66GLCQogBljY8kr1Qu3qn9WnOHPB4qMMcXGmHbgFeCy3hsYYz40xjQ7724AUizYr/JReTph2inLTo9ne3k97Z3ddpeiPJAVgT8WKO11v8z52EC+A7zd3xMicquIbBGRLZWVlRaUprxRbkktgQHCjBQdcDVUc1LjaO/s1hWwVL/cetFWRL4N5AC/6+95Y8yTxpgcY0xOUlKSO0tTHiSvpI6po6OJCAmyuxSv0zMNhfbHV/2xIvDLgdRe91Ocj32BiCwC7gMuNca0WbBf5YO6ug0FpXXafn+KRjkHYGlPHdUfKwJ/MzBRRMaLSAhwLbCy9wYiMgf4M46wP2rBPpWP2n24kaZ2HXA1HLPT4vQMX/Vr2IFvjOkE7gBWA4XAa8aYHSLyKxG51LnZ74Ao4K8iki8iKwd4OeXnNh+oASAnPcHmSrzXvPR4yutaKKttPvnGyq9Y0khqjFkFrOrz2AO9bi+yYj/K963fV83YuHBSEyLsLsVrLZgwAoANxTVcNVePo/qcjrRVHqO727BxfzULnYGlTs2kkdHERwSzobja7lKUh9HAVx5jz9FGaps7WJChgT8cAQHCgowRGvjqSzTwlcdYv88RUAsytP1+uBZkjKCstoXSGm3HV5/TwFceY0NxNakJ4aTEa7vzcC083o6vZ/nqcxr4yiM42u9rWDBem3OsMHFkFAmRIazXwFe96FBGi+2vaqKivoXWji5a2rtp6eiipaOL1vYupo+N1QuSA9h1uJG65g49PhYRERZkJLCxuAZjjM462o/2zm7e2naI2uYOwoMDCQ8JIDw4kDDnv0mjokmIDLG7TEtp4FukpLqZh1fv4p/bKk643VkTE/nZ4ilM14W5v6Cn6eE0vWBrmYUZI1i1/TBltS3azbWX7m7DP7Yd4r/f3UPJCa5xRIQE8t2zJ3DL2eN9ZpoP3/gubFTb1M7/fFDE8xsOEBQQwL9/NZMzMhOPnymEBwcSFhJAcEAAr+eW8b8fFnHJ/6zla7PG8JMLJpE+ItLub8EjrC+uJi0hgrFxuuCJVXp6O63fV62BDxhj+HhPJY+8s5udFQ1MHR3D8hvnMSc1/vNP4s7/j7V28vKmEv7w3h5e3HiQu86fxFVzUwgK9O5WcA38U9Ta0cXyTw/w2IdFNLV1cnVOKj86fxKjYsIG/Jqbz8rg6nmpPPlxMc+s3c/b2ytYMj+NH5w3kaToUDdW71m6uw2b9teweFqy3aX4lMyRUSRGhbChuJqr56We/At8WEFpHQ+9vYv1zo4Bj14zm0tnjSEgwNHUFUvwl77m7ElJbD1Yw4P/LOSeFdtZtm4/91w0hXMnj/TaJjIN/FOwvaye217YSnldC+dOTuKei6YyOTl6UF8bExbMTy6czPUL0/nj+3t5aVMJq7ZX8NfbFpKRFOXiyj3TzooG6ls6WDBBu2NaSUQ4LWME64ur/bodf0VuGT/+awEJESH84mtZfPO0dEKCBnemPjc9gde/dzrvfHaYh9/ZxU3Lt/CVSUn8zzfnEBP25T8Sns67P5/YYENxNUue2gDASzefxrM3zh902Pc2MiaMBy+fwaofnIUBrntmk98uPt3Tfq8Drqy3IGMEFfWtJ2yr9mXvFx7hp3/bxsKMEXx897nccMb4QYd9DxHhohmjWXPXV3jgkizWFVWx5MkNVB3zvkl/NfCHYM3OI1y/bBOjY8N4/Xunc3pm4rBfc3JyNM/dOJ+65nauX7aRuuZ2Cyr1LhuKaxg3IoLRsdp+b7WFGf7bH3/zgRpufzGXrNExPHl9DlGhw2vQCA4M4KYzx/PU0hz2VR7j6ifWU17XYlG17qGBP0grcsu47YWtTE2O5rXvLiQ5duC2+qGakRLLU9fncKCqmZuWb6a5vdOy1/Z0Xc75c/Ts3jUmJEWSGBV6fBSzvyisaOCm5ZsZGxfO8hvnDTvsezt38khe+M5pVB5r46r/+5Sio8cse21X08AfhGfX7eeu1wo4bXwCL96ygHgX9M09PTORP147m/zSOm5/MZeOLv9Yk7SwooHG1k7tf+8iPf3xNzj74/uDkupmrl+2iciQIJ6/+TRGRFnfISJnXAKv3rqQji7D1X9ez/Yy71hSUgP/BIwxPPreHn75j51ckDWKZTdYe6bQ10UzRvPg5TP4aHclP/lrAd3dvv8L+vn8ORr4rrJwwggON7RyoNr32/GPNrZy3bKNdHR18/x35ru0m2/WmBj+ettCwoMDWfLUBq/4FKWBfwJ/WLOHR9/by1VzU3j8W9mEBQe6fJ9L5qfx0wsn82b+IX711k6X789uG4qryUiMPGF3VjU8C/ykHb+htYMblm3maEMby26Yx8RRQ+9MMVTjEyN5/XunMzo2jKXPbmKjhx9jDfwBvLSxhD99UMQ1Oak8cuVMtw64uP2cCdx0xniWf3qAVdtPPHLXm3U5+9/r6FrXykiMJCk61OcD/xdv7mDPkUaeuG6uW9dETo4N49XvLiQ1Ppxb/rKFvUca3bbvodLA78f7hUe4/43tnDs5iQcvn358cIa7iAj3XjyFGWNjeeDNz6ht8s2eOzsO1dPYpu33riYiLMwYwfp91T7bjv/hrqOsyCvn9nMm8JVJSW7ff0JkCMtvnE9ocCA3PLuZIw2e2cVaA7+PgtI67ngpj2ljYvnfb2bbNpQ6KDCAR66aSV1zh8827Rzvfz9eB1y52oKMERxtbGN/VZPdpViuobWDe/++nUmjovj+VzNtqyM1IYJnb5hHbXM7Nzy7mcbWDttqGYgGfi8Hq5u4aflmEqNDWHbDPCJdeIF2MKaOjuH2czP5e145H+w6YmstrrB+XzUZSZGM1PZ7l+v5FOWL0yX/56pdHGlo5ZGrZhEa5PrrbCcyfWwsj38rmz1HGj2yt50GvlP1sTaWLttElzEsv3G+x8xtc8e5mUweFc29Kz6jwQPPGE5VZ1c3mw/UHh8YpFxr3IgIRsWEsqG4xu5SLPXpvipe3lTCzWdlMDs1zu5yADhn8kj+84oZfLK3inte3+5RzWga+EBLexc3/2ULFfWtPLM0hwkeNKdNSJCjaedoYyv/uWqX3eVYZsehBo61dWp3TDdx9Md3rHPrSQE0HM3tndzz+nbGjYjgR4sm2V3OF1ydk8qPFk3i9dwy/rBmj93lHOf3gd/VbfjhK3nkl9bxx2vnMDfd89qTZ6XGcfNZGby8qYRPi6rsLscS6/Y5vg8NfPdZmDGCysY2rxoZeiL/tdoxn/3DV84kPMTeppz+/OC8TK6dl8qfPijilU0ldpcD+HngG2P49Vs7eXfnER64JIvF0z13et67zp/E+MRIfrZim09MvbBm5xFmjI31mKYzf3DO5JEAvLvT+68HbT1Yy7Of7ue6Beke261XRPjN16dzzuQk7nvjMz7afdTukqwJfBFZLCK7RaRIRO7p5/lQEXnV+fxGERlnxX6H65m1+1n+6QFuPnM8N54x3u5yTigsOJCHrphBaU0Lv1u92+5yhuVwfSt5JXUe/QfWFyXHhjE7NY7VOw7bXcqwtHZ0cfffChgTG87PLppidzknFBQYwP9+M5spydF8/8VcPiu3dwqGYQe+iAQCjwEXAVnAEhHJ6rPZd4BaY0wm8Afg4eHud7hWba/gwVWFXDQ9mXsvnmp3OYNyWsYIrl+YzvJPD5BXUmt3OadszU5H4Fw4bZTNlfifC6cls62s3utmeezt8Q+L2FfZxG+vmOHSqU6sEhUaxLIb5hEbHsxNyzfbeuytOMOfDxQZY4qNMe3AK8Blfba5DHjOeftvwHli42oMWw/WcOer+WSnxfOHa2a7fWDVcNy9eApJUaH86q2dXnvx7Z0dh5mQFEnmSNcPfVdf1PNH9l0vPcsvq23miX8Vc9nsMbYMsDpVo2LCWH7TfFo6urjx2U3Ut9jT486KwB8LlPa6X+Z8rN9tjDGdQD3wpYY3EblVRLaIyJbKykoLSvuy/VVN3PzcFsbGhfPU9TlumR/HSlGhQfzkwsnkldTxj5MsmO6J6prb2VBcw4W6nKEtMpKimDQqymubdR55ZzcC/GyxZzfl9GfSqGj+/O257K9q4rbnt9Le6f4++h510dYY86QxJscYk5OUZP1f7+pjbdzw7CZEhGdvmEeCC6Y5docrs1PIGh3Dw2/vorWjy+5yhuS9wqN0dRttv7fR4mnJbNpfQ7WXrdiUW1LLyoJD3Hp2BmO8dLH70zMTeeSqmawvruZnr29z+6d0KwK/HOi9QnKK87F+txGRICAWcOuQv/qWDm5avpnD9a08vTSHcYmR7ty9pQIDhPsvmUp5XQvPrN1vdzlDsnrHYcbEhjFjbKzdpfitC6Yl023g/UL7e40MljGG37y1k6gvdlEAABGlSURBVKToUG77ygS7yxmWy+ek8OPzJ/H3vHJ+u6rQraFvReBvBiaKyHgRCQGuBVb22WYlsNR5+yrgA+PG77KuuZ3rntnIzooGHvtmtltn0nOV0yckcn7WKB7/sIjKRu84U2tu7+Rfeyq5YFqy3y6o7QmmjYkhJT6cd7yoWeetbRXkltTx0wsm2z7liRXu+Gom1y9M56lP9vPrt9wX+sMOfGeb/B3AaqAQeM0Ys0NEfiUilzo3ewYYISJFwF3Al7puukpNUzvffGojuyoa+fN1c1mU5Ts9Q+69eCrtXd38fo13dNP8eHclbZ3d2n5vMxHhwmnJrN1bxbE2zx/T0drRxUNv7yJrdAxXzk2xuxxLiAi/vHQaN54xjmXr9vPAmzvcsuCRJW34xphVxphJxpgJxpgHnY89YIxZ6bzdaoz5hjEm0xgz3xhTbMV+T6bqWBtLntzAvspjPLU0h69O8Z2wB8fiC9cvHMerm0sprGiwu5yTemfHYRIiQ5g3zvs/YXm7xdOTae/q5sNdnt+ss2zdfsrrWrj/kqkEelGPupMRER64JItbz87g+Q0Hue+N7S4PfY+6aGulow2tXPvkBkpqmnn2hnle1YVrKH7w1YnEhAfz4D/d2xY4VO2d3XxQeJRFU0faNuW0+lx2WjyJUSEe36xT2djG4x/u4/ysUZw+IdHuciwnIvz8oil8/9wJvLyplLtf30aXC0PfJ3/zDtc7wv5QXQvLb5zH6Zm+90bpERsRzJ3nTWRtURUfesDQ7YF8uq+KxrZO7Z3jIQIDhPOzkvlo11GP7un1+zV7aO3o4ucePqJ2OESEn1wwmTsXTeRvW8v48Wv5dLpoWmWfC/yK+haueXI9RxvbeP478z12ng0rfWtBOhlJkfzmn4UeN/92j9U7DhMZEuiTZ2ne6sJpo2hq72Kdh07It+twA69uLuH6hePI8KAZbF1BRLhz0SR+euFk3sg/xA9fzXfJmb7PBX50WDATkqJ44ebTPHLmS1cIDgzgvounUlzZxIsbDtpdzpd0dRvW7DzCuVNGet1AN192+oREokODPHIQlqMbZiHRYcH84Dz7VrFyt++fm8m9F09h/IhIXHG5wvv7N/XRM2+Fv/nqlJGcmZnIo+/v5etzxhIX4TmDyrYerKXqWLv2zvEwIUEBfHXqSNbsPEJnV7dHXVv5YNdR1hZV8R9fy/Ko97I73Hq268YZeM5PWA2LiGMwVkNLB398f6/d5XzB6h2HCQkM4NwpI+0uRfWxeFoytc0dbD7gOZPxtXd28+A/C5mQFMm3F6TbXY5P0cD3IVOSY1gyP43n1x/0mEUujDG889lhzpyY6BUzG/qbr0xOIjQowKOadZ7fcJDiqibuvySLYA/61OEL9Gj6mLvOn0R4cCC/XVVodymAYynD8roWFmtzjkeKCAni7ElJrN5x2CO69dY0tfPH9/bwlUlJnDtZPxFaTQPfx4yICuUH503kg11H+XiPa2YcHYrVOw4TIPjUCGdfs3haMhX1rWwrs3dxDoBH39tDU3sX9/+bd6xR4W008H3Q0tPHMW5EBL95a6fL+vMORltnF69tKeWMzESvnZnUHyyaOorQoABe2mjvuqt7jjTy4sYSvn1aGhNH6VoJrqCB74NCggK49+Kp7D16jJdsXDz5jbxyjjS0cctZGbbVoE4uNiKYa+alsiKvjIp6e1Zj6llfOjIkkDsXTbKlBn+gge+jHEPRR/D7NXuob3b/6jpd3YYnPi5m2pgYzpqog6083S1nZdBt4OlP7Jlu+8PdR/lkbxV3LppEvH4adBkNfB8lIvy/S7Js66b5zmeH2V/VxO3nZOpUyF4gNSGCS2eN4eVNJdQ2tbt13x1d3fzmrUIykiK5bqF2w3QlDXwfNnV0DNfMS+Mv6w+wr9J93TSNMfzfx0VkJEbq3Dle5HvnTKC5vYvn1h9w636fX+/shvlvU7Ubpovp0fVxP75gEmHBgfxi5Q63dbv7ZG8Vn5U38N2vZPjUdLa+btKoaBZNHcXyTw/Q5KZ58o82tPLoe3s4a2KidsN0Aw18H5cYFcrPFk/mk71VvOCmXhiPf1REckwYX5/Tdy175eluP3cCdc0dvOyGi/3GGO5+fRvtXd384tJp2vTnBhr4fuDbC9I5e1ISv/1nIcUubtrJLallQ3ENN581ntAgnSjN22SnxXPa+ASe/mQ/bZ2unTb5xY0lfLS7knsvnsoEH58N01No4PsBEeF3V80kJCiAH71W4NK++Y9/uI+4iGCWzE9z2T6Ua91+biaHG1p5I6/cZfsorjzGg/8s5OxJSVyn8+W4jQa+nxgVE8aDl0+noLSOxz7c55J97DnSyHuFR1i6cJxPLDTtr86emMi0MTH8+eNil8zJ3tnVzY9eKyAkKIDfXTVTm3LcSAPfj1wycwxfnz2GP32wl4LSOstf/4mP9hEeHMgNp4+z/LWV+4gIt5+TSXFVk0smVXvsw30UlNbx4OXTGRUTZvnrq4Fp4PuZX142nZHRofzo1Xxa2q1roy2taebNgkMsmZ+mA2d8wOLpyYxPjOTxj4os7d1VUFrHnz7Yy9dnj+GSmWMse101OBr4fiY2PJj//sYsiquaeOht62bUfOqTYgIEbjl7vGWvqewTGCB89+wMPitv4JO91iyB2NLexY9ey2dkdCi/vGy6Ja+phkYD3w+dnpnITWeM57n1By2ZUfOtbYd4YcNBrpqbwujYcAsqVJ7g8uyxjI0L52evb6O0pnnYr/fQ24UUVzbxX9+YRWx4sAUVqqHSwPdTdy+ezMSRUdz1aj75w2jPf3fHYe58JZ+c9AT+3yVZFlao7BYaFMjTS3No6ehiyVMbOFR3ahOrGWN4dt1+nlt/kJvOGM8ZmTq3kl2GFfgikiAia0Rkr/P/+H62mS0i60Vkh4hsE5FrhrNPZY2w4ECeuG4uEaGBXPPn9awsODTk1/h4TyV3vJTH9LGxPHNDDhEh2jPH10wdHcPzN51GfXMH33p6I0cbWof09R1d3dz3xmf88h87OT9rFHcvnuyiStVgDPcM/x7gfWPMROB95/2+moHrjTHTgMXAoyISN8z9KgtMSIrize+fyayUOH7wch6/X7OH7kF2w/t0XxW3/mULmSOjeO7G+USH6Ud0XzUjJZblN83jSEMr33p6I9XH2gb1dXXN7SxdtomXNpbwvXMm8OdvzyUsWAfj2Wm4gX8Z8Jzz9nPA1/tuYIzZY4zZ67x9CDgKJA1zv8oiCZEhPH/zfL4xN4U/vb+Xf38l76S9d7YcqOHm57aQPiKCF24+jdgIDXtfNzc9gWeWzqOkppnrntl00im391Ue4/LHP2XLgVr++xuz+NniKQTovEq2G27gjzLGVDhvHwZOuI6diMwHQoB+R/6IyK0iskVEtlRW2r88n78IDQrkkatmcu/FU1i1vYJrnlzPkQE+um8rq+PGZzeTHBPGCzefpitZ+ZGFE0bw1PU5FB09xvXPbqKxtf/QX7u3issfW0dDSwcv3XIaV85NcXOlaiBysj62IvIe0N8ct/cBzxlj4nptW2uM+VI7vvO50cBHwFJjzIaTFZaTk2O2bNlyss2Uxd7beYQfvpJHQIAwIjKEzm5DV69/Da0dJMeG8dp3F2qPHD/13s4j3PbCVkKCAogICSQwQAgKCCAwQAgMEEpqmslMiuLppTmkJkTYXa7fEZGtxpicfp8bzqAKEdkNnGOMqegJdGPMl67KiEgMjrD/rTHmb4N5bQ18+xRWNPDUv4rp7DYEOX+JgwId/4cHB7L09HGkxOsvsj9bu7eKd3cePn4i0Nnr/6SoUO66YBJROr2GLVwZ+L8Dqo0xD4nIPUCCMebuPtuEAG8D/zDGPDrY19bAV0qpoTtR4A+3Df8h4HwR2Qssct5HRHJE5GnnNlcDZwM3iEi+89/sYe5XKaXUEA3rDN+V9AxfKaWGzpVn+EoppbyEBr5SSvkJDXyllPITGvhKKeUnNPCVUspPaOArpZSf8NhumSJSCRwcxkskAtYs1WMtrWtotK6h0bqGxhfrSjfG9DtBpccG/nCJyJaB+qLaSesaGq1raLSuofG3urRJRyml/IQGvlJK+QlfDvwn7S5gAFrX0GhdQ6N1DY1f1eWzbfhKKaW+yJfP8JVSSvWiga+UUn7CqwNfRL4hIjtEpFtEcvo893MRKRKR3SJy4QBfP15ENjq3e9W5WIvVNb7aax2AAyKSP8B2B0Rku3M7l88LLSK/EJHyXrVdPMB2i53HsMi5yI2r6/qdiOwSkW0i8ncRiRtgO7ccr5N9/yIS6vwZFznfS+NcVUuvfaaKyIcistP5/v9hP9ucIyL1vX6+D7i6Lud+T/hzEYc/OY/XNhHJdkNNk3sdh3wRaRCRO/ts45bjJSLLROSoiHzW67EEEVkjInud/w+0TOxS5zZ7RWTpKRVgjPHaf8BUYDKO5RNzej2eBRQAocB4HIumB/bz9a8B1zpvPwF8z8X1/jfwwADPHQAS3XjsfgH85CTbBDqPXQaOxecLgCwX13UBEOS8/TDwsF3HazDfP3A78ITz9rXAq2742Y0Gsp23o4E9/dR1DvCWu95Pg/25ABfjWAFPgAXARjfXFwgcxjE4ye3HC8diUNnAZ70eewS4x3n7nv7e80ACUOz8P955O36o+/fqM3xjTKExZnc/T10GvGKMaTPG7AeKgPm9NxARAb4K9Kyx+xzwdVfV6tzf1cDLrtqHC8wHiowxxcaYduAVHMfWZYwx7xpjOp13NwAprtzfSQzm+78Mx3sHHO+l85w/a5cxxlQYY3KdtxuBQmCsK/dpocuAvxiHDUCccz1sdzkP2GeMGc4o/lNmjPkXUNPn4d7voYFy6EJgjTGmxhhTC6wBFg91/14d+CcwFijtdb+ML/9CjADqeoVLf9tY6SzgiDFm7wDPG+BdEdkqIre6sI7e7nB+rF42wMfIwRxHV7oJx9lgf9xxvAbz/R/fxvleqsfx3nILZxPSHGBjP08vFJECEXlbRKa5qaST/Vzsfk9dy8AnXXYcL4BRxpgK5+3DwKh+trHkuHn8svIi8h6Q3M9T9xlj3nR3Pf0ZZI1LOPHZ/ZnGmHIRGQmsEZFdzrMBl9QF/B/waxy/oL/G0dx003D2Z0VdPcdLRO4DOoEXB3gZy4+XtxGRKOB14E5jTEOfp3NxNFscc16feQOY6IayPPbn4rxGdynw836etut4fYExxoiIy/rKe3zgG2MWncKXlQOpve6nOB/rrRrHx8kg55lZf9tYUqOIBAFXAHNP8Brlzv+PisjfcTQnDOsXZbDHTkSeAt7q56nBHEfL6xKRG4BLgPOMswGzn9ew/Hj1YzDff882Zc6fcyyO95ZLiUgwjrB/0Rizou/zvf8AGGNWicjjIpJojHHpRGGD+Lm45D01SBcBucaYI32fsOt4OR0RkdHGmApn89bRfrYpx3GdoUcKjmuXQ+KrTTorgWudPSjG4/hLvan3Bs4g+RC4yvnQUsBVnxgWAbuMMWX9PSkikSIS3XMbx4XLz/rb1ip92k0vH2B/m4GJ4ujNFILj4/BKF9e1GLgbuNQY0zzANu46XoP5/lfieO+A4730wUB/pKzivEbwDFBojPn9ANsk91xLEJH5OH7XXfqHaJA/l5XA9c7eOguA+l7NGa424KdsO45XL73fQwPl0GrgAhGJdza/XuB8bGhcfVXalf9wBFUZ0AYcAVb3eu4+HD0sdgMX9Xp8FTDGeTsDxx+CIuCvQKiL6lwO3NbnsTHAql51FDj/7cDRtOHqY/c8sB3Y5nzDje5bl/P+xTh6gexzU11FONoq853/nuhblzuPV3/fP/ArHH+QAMKc750i53spww3H6EwcTXHbeh2ni4Hbet5nwB3OY1OA4+L36W6oq9+fS5+6BHjMeTy306t3nYtri8QR4LG9HnP78cLxB6cC6HBm13dwXPN5H9gLvAckOLfNAZ7u9bU3Od9nRcCNp7J/nVpBKaX8hK826SillOpDA18ppfyEBr5SSvkJDXyllPITGvhKKeUnNPCVUspPaOArpZSf+P85+ubUAXvBuAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-10,10)\n",
    "y = sin(x)/x\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C6. **DO EXERCISE.** Based on the graph in C5, what is the value of the limit $\\displaystyle \\lim_{\\textstyle x{\\to}0} \\frac{\\sin x}x$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# RECORD YOUR ANSWER: the limit is 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the limit with a table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C7. \n",
    "The other thing we can try is making a table.\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.84147098],\n",
       "       [0.1       , 0.99833417],\n",
       "       [0.01      , 0.99998333],\n",
       "       [0.001     , 0.99999983]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = r_[1, .1, .01, .001] # Make array of numbers approaching 0 from right\n",
    "y = sin(x)/x             # Plug the array into our function\n",
    "c_[x,y]                  # Make a table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.        ,  0.84147098],\n",
       "       [-0.1       ,  0.99833417],\n",
       "       [-0.01      ,  0.99998333],\n",
       "       [-0.001     ,  0.99999983]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = r_[-1, -.1, -.01, -.001] # Same but approaching from left\n",
    "y = sin(x)/x\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that to display two tables, we use two code cells, because Jupyter only displays one output per cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C8. **DO EXERCISE.** Based on the table in C7,\n",
    "what is the value of the limit $\\displaystyle \\lim_{\\textstyle x{\\to}0} \\frac{\\sin x}x$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# RECORD YOUR ANSWER: the limit is 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simplify the code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C9. We can simplify the code for `x` using an array.\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.84147098],\n",
       "       [0.1       , 0.99833417],\n",
       "       [0.01      , 0.99998333],\n",
       "       [0.001     , 0.99999983]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = .1 ** r_[:4]\n",
    "y = sin(x)/x\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should get the same table as in C7.  \n",
    "Why does this work?\n",
    "Because `.1 ** r_[:4]` means \"$0.1$ raised to the $0,1,2,3$,\" which is going to be $1,0.1,0.01,0.001$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Increase precision\n",
    "\n",
    "C10. The arrays we have made so far show (up to) 8 decimal places.  \n",
    "As an example, let's change the number of decimal places displayed to 17 decimal places:\n",
    "\n",
    " _RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.                , 0.8414709848078965],\n",
       "       [0.1               , 0.9983341664682815],\n",
       "       [0.01              , 0.9999833334166665],\n",
       "       [0.001             , 0.9999998333333416]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set_printoptions(precision=17)\n",
    "\n",
    "x = .1 ** r_[:4]\n",
    "y = sin(x)/x\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you run this cell, from now on, arrays will display (up to) 17 decimal places."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Turn off scientific notation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C11. Arrays with very small numbers (less than 0.001)\n",
    "will automatically change to scientific notation.\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.0000000000000000e+00, 8.4147098480789650e-01],\n",
       "       [1.0000000000000001e-01, 9.9833416646828155e-01],\n",
       "       [1.0000000000000002e-02, 9.9998333341666645e-01],\n",
       "       [1.0000000000000002e-03, 9.9999983333334164e-01],\n",
       "       [1.0000000000000002e-04, 9.9999999833333342e-01]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = .1 ** r_[:5]\n",
    "y = sin(x)/x\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C12. We can turn off scientific notation for arrays using `set_printoptions`\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.                , 0.8414709848078965],\n",
       "       [0.1               , 0.9983341664682815],\n",
       "       [0.01              , 0.9999833334166665],\n",
       "       [0.001             , 0.9999998333333416],\n",
       "       [0.0001            , 0.9999999983333334]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set_printoptions(suppress=True)\n",
    "\n",
    "x = .1 ** r_[:5]\n",
    "y = sin(x)/x\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C13. **DO EXERCISE.**  \n",
    "(1) Use the graphical approach to find\n",
    "$\\displaystyle \\lim_{\\textstyle x{\\to}0^{\\textstyle+}} x^{\\textstyle x}$.\n",
    "\n",
    "(2) Use the numerical approach (make a table) for the same limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13905d10>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (1) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(0,2) # Or any interval starting at 0\n",
    "y = x**x\n",
    "plot(x,y)\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.                , 1.                ],\n",
       "       [0.1               , 0.7943282347242815],\n",
       "       [0.01              , 0.954992586021436 ],\n",
       "       [0.001             , 0.9931160484209338],\n",
       "       [0.0001            , 0.9990793899844618],\n",
       "       [0.00001           , 0.9998848773724686],\n",
       "       [0.000001          , 0.9999861845848758],\n",
       "       [0.0000001         , 0.9999983881917339],\n",
       "       [0.00000001        , 0.9999998157932095],\n",
       "       [0.000000001       , 0.9999999792767343]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (2) TYPE YOUR CODE:\n",
    "\n",
    "x = 0.1 ** r_[:10] \n",
    "y = x**x\n",
    "c_[x,y]\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a function\n",
    "\n",
    "C14. Example. Let's make a graph and make tables to find\n",
    "$\\displaystyle \\lim_{\\textstyle x{\\to}0} \\frac{1-\\cos x}{x^2}$  \n",
    "We will use `def` to store the function so we don't have to type the function over and over.\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return (1 - cos(x))/x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed139f2e90>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1,1)\n",
    "y = f(x)\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.                 , 0.45969769413186023],\n",
       "       [0.1                , 0.49958347219742893],\n",
       "       [0.01               , 0.4999958333473662 ],\n",
       "       [0.001              , 0.4999999583255031 ],\n",
       "       [0.0001             , 0.49999999696126435],\n",
       "       [0.00001            , 0.5000000413701853 ],\n",
       "       [0.000001           , 0.5000444502911701 ],\n",
       "       [0.0000001          , 0.4996003610813201 ]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 0.1 ** r_[:8]\n",
    "y = f(x)\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.                 ,  0.45969769413186023],\n",
       "       [-0.1                ,  0.49958347219742893],\n",
       "       [-0.01               ,  0.4999958333473662 ],\n",
       "       [-0.001              ,  0.4999999583255031 ],\n",
       "       [-0.0001             ,  0.49999999696126435],\n",
       "       [-0.00001            ,  0.5000000413701853 ],\n",
       "       [-0.000001           ,  0.5000444502911701 ],\n",
       "       [-0.0000001          ,  0.4996003610813201 ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = -0.1 ** r_[:8]\n",
    "y = f(x)\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the graph and the tables tell us that $\\displaystyle \\lim_{x\\to0} \\frac{1-\\cos x}{x^{\\textstyle2}} = 0.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taking the limit as $x$ approaches a number other than zero\n",
    "\n",
    "C15. Example.\n",
    "Let's investigate\n",
    "$\\displaystyle \\lim_{\\textstyle x{\\to}\\pi/2} \\left(\\frac\\pi2 - x\\right) \\tan x$\n",
    "\n",
    "Notice that in this example, $x$ is not approaching 0.\n",
    "\n",
    "_RUN the following._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return (pi/2 - x)*tan(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13adead0>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0,pi)\n",
    "y = f(x)\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.5707963267948966, 0.6420926159343308],\n",
       "       [1.6707963267948966, 0.9966644423259243],\n",
       "       [1.5807963267948966, 0.9999666664444484],\n",
       "       [1.5717963267948964, 0.9999996666667056],\n",
       "       [1.5708963267948965, 0.999999996667279 ],\n",
       "       [1.5708063267948966, 0.9999999999727899],\n",
       "       [1.5707973267948965, 1.000000000060899 ],\n",
       "       [1.5707964267948966, 1.0000000006123202]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = pi/2 + 0.1 ** r_[:8]\n",
    "y = f(x)\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5707963267948966, 0.6420926159343306],\n",
       "       [1.4707963267948965, 0.9966644423259232],\n",
       "       [1.5607963267948965, 0.9999666664444362],\n",
       "       [1.5697963267948967, 0.9999996666665832],\n",
       "       [1.5706963267948966, 0.9999999966660543],\n",
       "       [1.5707863267948965, 0.9999999999605436],\n",
       "       [1.5707953267948966, 0.9999999999384342],\n",
       "       [1.5707962267948965, 0.9999999993876733]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = pi/2 - 0.1 ** r_[:8]\n",
    "y = f(x)\n",
    "c_[x,y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph and the tables tell us that $\\displaystyle \\lim_{\\textstyle x{\\to}\\pi/2} \\left(\\frac\\pi2 - x\\right) \\tan x = 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Exercises\n",
    "\n",
    "C16. **DO EXERCISE.**  \n",
    "Let $f(x) = x \\ln x$.  \n",
    "(1) Plot a graph of $f(x)$ over the interval $(0,1]$\n",
    "and based on your graph, estimate\n",
    "\n",
    "$\\qquad\\displaystyle\\lim_{\\textstyle x{\\to}0^+} f(x)$.\n",
    "\n",
    "(2) Use the numeric approach to find the same limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13bbe5d0>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (1) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(0.0001,1)\n",
    "y = x*log(x)\n",
    "plot(x,y)\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.                 ,  0.                 ],\n",
       "       [ 0.1                , -0.23025850929940456],\n",
       "       [ 0.01               , -0.04605170185988092],\n",
       "       [ 0.001              , -0.00690775527898214],\n",
       "       [ 0.0001             , -0.00092103403719762],\n",
       "       [ 0.00001            , -0.0001151292546497 ],\n",
       "       [ 0.000001           , -0.00001381551055796],\n",
       "       [ 0.0000001          , -0.0000016118095651 ],\n",
       "       [ 0.00000001         , -0.00000018420680744],\n",
       "       [ 0.000000001        , -0.00000002072326584],\n",
       "       [ 0.0000000001       , -0.00000000230258509],\n",
       "       [ 0.00000000001      , -0.00000000025328436],\n",
       "       [ 0.000000000001     , -0.00000000002763102],\n",
       "       [ 0.0000000000001    , -0.00000000000299336],\n",
       "       [ 0.00000000000001   , -0.00000000000032236],\n",
       "       [ 0.000000000000001  , -0.00000000000003454],\n",
       "       [ 0.0000000000000001 , -0.00000000000000368]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (2) TYPE YOUR CODE:\n",
    "\n",
    "x = 0.1 ** r_[:17]\n",
    "y = x*log(x)\n",
    "c_[x,y]\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C17. **DO EXERCISE.**  \n",
    "(1) Define the python function $f(x) = x^{\\textstyle-1}e^{\\textstyle-1/x}$  \n",
    "(2) Plot the function $f(x)$ over the interval $(0,1]$ and estimate.  \n",
    "\n",
    "$\\qquad \\displaystyle\\lim_{\\textstyle x{\\to}0^{\\textstyle+}}f(x)$  \n",
    "\n",
    "(3) Use the numeric approach to find the same limit.    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (1) TYPE YOUR CODE:\n",
    "\n",
    "def f(x): return x**-1 * exp(-1/x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13c21810>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (2) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(0.0001,1)\n",
    "plot(x,f(x))\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.                 , 0.36787944117144233],\n",
       "       [0.1                , 0.00045399929762485],\n",
       "       [0.01               , 0.                 ],\n",
       "       [0.001              , 0.                 ],\n",
       "       [0.0001             , 0.                 ]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (3) TYPE YOUR CODE:\n",
    "\n",
    "x = 0.1 ** r_[:5]\n",
    "c_[x,f(x)]\n",
    "\n",
    "# RECORD YOUR ANSWER: the limit is 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C18. **DO EXERCISE.**  \n",
    "We wish to find the limit of the oscillating function\n",
    "\n",
    "$\\qquad f(x) = x \\sin \\frac1x$\n",
    "\n",
    "as $x$ approaches 0.\n",
    "\n",
    "(1) Plot the function $f$ over the interval $[-\\pi,\\pi]$ using 10000 points for $x$.  \n",
    "(2) \"Zoom in\" by replotting the function over $[-0.1,0.1]$.  \n",
    "(3) Motivated by the squeeze theorem, plot on the same axes the function $f$ over $[-0.1,0.1]$ as well as $y=|x|$ and $y = -|x|$.  \n",
    "(4) Estimate the limit as $x\\to0$.  \n",
    "(5) How did graphing the absolute value help you find the limit in (3)? (Choose one)  \n",
    "_The mean-value theorem_\n",
    "$\\quad$ _The function is continuous_\n",
    "$\\quad$ _The squeeze theorem_\n",
    "$\\quad$ _They didnt; I just guessed_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13d66b50>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (1) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(-pi,pi,10000)\n",
    "y = x*sin(1/x)\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed13e92b90>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JZBy/143BkKQ2tulm2h011LOcXk/B7aKGdyvRgBceFzVkqqnHupI93B+s1AjimTyy+aKl1zu9kcL2/gB2DARa0pFK4AynN9IgAi7ZNdCQQF9JZDAULr+mvG4XBoOSoxrBSLgxQQDIYdPCRyBwjNNK8S23y3p8MyBnPg6FJTUSw07Wk4pGEKjUCABgzWKZCV5WYDzq7wk1u1uZ30hhJOzDRDSAlUQGjFmLHFrezJaFjnJGIj5HNIKleGMF57RMRP1CIxA4x3wsbblZhp7hsM+RsDsuCKI6QcDV+hWL7zkfS2Osz99w1JGgM5jbkEOKRyJy3SkrtfoLRYa1ZKVpCJAFgRMawWI8AxcBQ6EmNIKovyeSKIUgaBMLyuLYDENhnzMaQSqLiN8Dj7v88uAagZXFnDGGtWQOQyEJgyEv1pK5uhVMre40Bc1jpqrsWlLe0Tfin9pM58EYEA1WCoKBoKSaI+1kKZ7BUNjXsNYNyKah1UQW6Vx3J5UJQdAmFmOZplRWABgOSY5pBHpHMQDVvruSML8AJLMFZPNF9AclDIZ8KBQZYunqO0nGGN7xT4/g/V992vrEBQ3xb48cx+V3PFRXwK8nc4gGvKrN3Yog4N95n78yPmUwJDmiKS7FM035B4BSjS0nS753AkIQtIFEJo94Jt+0RjAc8WF507qtth7rySz6A5U7t0FFxV6z8KPl/oTBkLdkWqrx/LmNNB6bWcXXn5wVvQ9axKf+8yXMx9J47NhKzXEbKUUQROTv0Yo5h5uR+gKVG4yBoIR4Oo9cwVoQQj2WE9kK57RVeiWXQAiCNsAdpmNNagRDIQmZfBEJm2uhrFXRCPhubiNlvqzFWkJeAAaCUsnZXEMQnFwtRRUtW9A8BI2TVwTuidXqEV35QhHxdB79QS+iyiYhZsFHEE/L10zEUCOQrzWrQQj1WE1kDH0SVlCr7na5n0AIgjbAs4HHGgwd5fAIjGWbcwk2UrmK0FFArjcUktyWnIT8xz0QkjAQ5FFH1Z+vDUsUOQfOk80X1XpVtc53TFnIowGvGkSwXuN7rHw+Nw0ZaATqBsHeRvGrm9myukaNwAVBt0cOCUHQBhbVsLZmncXWbfZmkE1DlT9YQF4IGhIEQUndDcZr+AgWNULNiglK0BjrqSy4ZXG5hqlnQ5NkKHlcCFrcEHDtwUgQDAYbC0uuRTpXQCJbULXQRgn7PIj4PF2fSyAEQRvgpqFxG8JHAWApbt8PqFiUwwIHDExDgGzjtSQIElwQeDWCoLppKZktPWakOTDGkHCo4mo3k84VDH1JWvNOrR0+j+rh2kA04FUz0M3Av/O+QKVpaMCEydAq1cqkNMJ41C98BAL7WYhlEJLcDXUm08IFgZ0aQTydR7FKmB8gLwBWbMNryRyI5OdFlN1gLY0gkSn5O4xCCv/1p8dx3ofv6/odmt289bM/xq1ffKLiOF/8JY+rpsmOC3/uH7CqGXLTkNE1zxdrO/thc0HQrEYA8FyC7vZXCUHQBuzIIQBKF7nVBK9arKeU8hI2mob6/F543C5IHhd8HpdqbzYimZWrRbrIeIf6uR8dRZEBh05vmJ5Dr7MYS+PwfBz3v7BQ8Rj/LqeGgjVj+Td09aeiAS82rPgIUnmEJHdFbor8mvZrBDwyrdmoIUDOLp4XGoHAbuzIIQDkXVw04K1p27UK3xUOhKoLglp5AHri6XxZhnLE762tEWQLCPs8iAa8NW3Gp4VGYBqt30VvHuIL/M7BUM3zXdII5O+yP2htQxBP5wxDRwH5Oo74PFi10VnMEy0Hm8gq5oxHA1iMZ2wPb+0khCBoA/M2aQSA3ELSVo1AtQVXNw1ZWwDyZeaAPr+ntkaQySMouRH2ewx9AR6XfMkKR7J5tN9XXHdOS4IgiHSuWLVlpD78sxHTkJGjmDMQkmx1FttqGurzg7Fygdpt2CIIiOhGInqJiI4QUUXTGSLyEdFXlMcfJaIp5fh1RPQEET2n/L/ajvl0Mowx20xDgFxmws46LXoTgJ5owItktmB6d7SZySGsiR2P+D01ncWJbB4hyYOQ5DHMj+Chjlo/RTpXwG988SAeOVo7IaoXWIpn8CufexQzmr4PWhOb3pzDv+9tSl8MrY9GSyKTh9dN8HnkpjL9QUk1I5ohns4b5hBwBmzOLl5JZOF1k2Ems1XGo841z+kUmhYEROQG8FkAbwBwLoB3EdG5umHvAbDGGNsD4NMAPqkcXwbwc4yx8yC3svxis/PpdGKpPDL5YsPt8/SM2FxvqBTlY7yT4uq92d3gZiaPiE8rCGqbhpLZAoI+N0K+So2AMaYuZFphcng+jvsOLeBj33nB1Jy6mftfWMCPjizjcz86qh7TLtj6Htfcds+/12oRWYlMHkGpXLOrpUHoidUwDQHAYLC2KdAqq5tZDAQlEDVeZ4jDS8U70Q2wU7BDI7gUwBHG2FHGWBbAlwHcpBtzE4C7lNtfA3ANERFj7CnG2Gnl+CEAASKyZ4XsUBbiPKvYLo2gsfaR1VhX472Nd1JRq4IgnbekESSzBVkj8FVqBOlcEVlFE9H6KVaVqCkrCU7dCl9M/Z5SO0jtedELglQuj6DPo5rv9I9zuO+Gw29X0yD0xFL5mrvzgaD9GoEdZiGg9Ft1ohtgp2CHINgO4KTm/inlmOEYpcfxBoAh3ZhfAPAkY8xQ7BLRrUR0kIgOLi0t2TDt9mBXDgFnOOzDejJnuVlMNdaTOfQZVB7lWBYEmXIfQcTvqRl+qvoIfG4kq9izgXJBwH0kLs2U/+XHx3BU0yKzW4mlc/jbB6fV/Av+P6Wplqk9VxWCIFtAwCtrYEA9jaAkXML+2hqEnng6p4YPGxG16Hyux6pBE5xGGQpJcLuoq3tpdISzmIj2QzYX/Ua1MYyxOxljBxhjB0ZGRlo3OZuxq7wEh+967Crju57MGpaX4Fg1DcV1GkHYJ/sYqpHIFhCU3AhKlaYhbbKZ9jX4LtilmAFWNjP48LdfwLs//5ipOW5lvvr4SXzq/pfx7WdkxTqTkzcE2mQvfgyQNTQtSeV8h33yIl9LIwgZaAS1tDsOYwyxdN4wmYwTDXgRT+dRsKnQ4Goia0vEEAC4XISRsDPNczoFOwTBLIAdmvuTyjHDMUTkARAFsKLcnwTwDQD/nTH2ig3z6Wj4rsKO8FEApip6WmE9ZVxwjsM1AjNJZdl8EZl8scxHEPK5kcjmq1ZMTWZLpgq9aUi7y01pHttUzBNcEMyuyzHfPKyWMdZ1PQ74gskDBXg58oyiGWrPj7aWfqVpqAB/mUZQ3Vkc8pU0Au74rSY4tCSzBRSKrGbUkJXrygwrCeMmOI0y1ufDgogaqsnjAPYS0RlEJAF4J4C7dWPuhuwMBoC3AXiIMcaIqB/APQBuY4z92Ia5dDwLsTSiAS/8Xnf9wSYYaKBZTC3kyqPVf0BWfrB8kdCahoKSB4zJ9n492XwRuQJDSHIjKLmRyJQLDL6gDYakssWNOyz5Mb4Y8v/XffoHuOWug3Xnu1X4jydO4bJPPIhkNq/u9rkQ5OdCqz2lc6WaO3qNQDUNSfVNQyFJK9C5IKh/HZRCT6sLAr75sMM8lM3LlVLt8hEAcl0wETVUA8Xm/z4A9wF4EcBXGWOHiOijRPQWZdjnAQwR0REA7wfAQ0zfB2APgNuJ6Gnlb7TZOXUycuioff7wIZsFwUaNgnOANR8BX3TCmgWA7yoT2coFhy9eQcVZnC8y1TkMlIRHf9Bbph3wxZAfy+iEzJHFTTx4eLHufLcK//Bfr2B5M4PZtZSqGfBzx89RuUZQVGtHpXKVWlZQU+6kumko37BpSK08Wsc0BMBS/aJqlHpg2CgIIr6u9hE0H2QLgDF2L4B7dcdu19xOA3i7wfM+DuDjdsxhq7AQy9gWMQQ01j6yFvVMQ5LHBb/XZWoBiGcq68vwEMRkpgCEy8dzU1DI5wbvLpjMFNTYdb64DQSlstLbfBfMH88WKrUFAHhxLoY3/+2PcM/vvg5nj/fVnX8nkS8U8bpPPozfuPJM9dxsZvJqkAD/PtRzodOYQj4PvG6qFATZAvxSfWdxMlMwNA2ZiRqqVXmUwxMY7dAIePCAvaYhP9aSOWTypeuxm+gIZ3EvsRhLq3HJdtAflEBkj4+goFQerWUaAuQftJkyE5sGzUhCUg2NIFPSCIIGO1S+iA0EJaQ1UVJcA8jkiygWWZlGkNGM+8rjJ1EoMvxoehkHZ1a3TAe0p06sYW4jjflYGh+/50U1uzqRKagaE9cI+OdN6jQCv8cNv9dd0Xs3lSsg6HVD8rgguV3YNPheAPl70JqGwg2ZhkxoBDYEPaiVR5vsRaCFa/FW2nNuJYQgaCHFIsNiPGOracjtIvQHvLaUXIinc2CsesE5Tl/Ai5iJLmWGPgLldtLQNFTSCAKKD0W7o0+rgsCLbL6omkXS2jH5QtnibxRW+9TJdbztH3+Kz//oWN3P0G5mlhP4+b//CT7y7UMAZGHtdcsqQSKbV88P/5z8HJWZhvIF+LwuRRCUn49UroCAIpxDPrehRpAvyE7/UJlm5wZRpc/BiJJpqDXOYl6N124fAdC9SWW2mIYE5lhNZpEvMttyCDh2pefzxKNapiFATjYz5SPggsBIIzAwKXAtIeD1gLsGUlmtj6DkLOb3Qz5PmQaQyhbKhIdWEPAkU94O8x/+6xV85eBJfPt9r1MXw07id770lPqZDx5fU4+7FNtQKltQP5/eQa7XCIZCsnDVawTJbEkQBCWPYWgvN9lp8wiICGHJU1G7yAhzpiHrXc+qYWcvAg6vBNCtDmMhCFoIr6Fvp2kIkC94OwSBtptYLfoCXlPvp5oEjHwEhqahkkZgtNtXTUPKDzzFBYFmsU9myzUC7W0eWcPLDqwmslhNZPHBbz6Ht1+yA6/Zrc9xbA/HVxL4+4dfUXMDAOOdd1bZqQMaQaBxnDPGQETI5Arwe2XfjlYQFIoM2XxR1b5CPrf6HWjh35W+l0C1woB6YiZMQ410PavGaiILt4vKqt42Sym7uDs1AmEaaiGLcXua1usZtEsj4KWG62oE5prTGGoEvvoaQVDyICDJl6bWxMG1AzUCJlseNgrIpqRsmSAoPVZUQlELxXLzyNefnMW7/r9H8MVHjtf9TE7z8EuLuPIvvo+vHDxZdjxv4M/geRr8NlAuOHMFRZgquQIBr7s8FyNXvtMPSh5D3w1f7IN6QeDzmMojiKVzSpBBba2r32JF02qsJLIYCHpVzckOBoMSPF2cXSwEQQtRs4ptjBoCZEFgh7OYO+rq+whql5LmbKbzcBHUHSdQRyPQ+Ah4ZIZ2kU/nC5DcLvU19HkD8rFi2X3tjtUo2UrLn3zzeXzg68/V/VxO8fkfHcOv/fPjdcfx1IpsvqgxDVWGzqr5Ffki/F4XfDrTED8PZRqBkWlIEdphX/lCHq5TN4oj1xmqvzvvs9j+shqrm/bVGeK4XKSEkAqNQNAkfDcxYlPlUc6gUsu92exZbp+taxpSNIJ678frDGkrQJbyCIwWHK1GoISM6hYuv9elLlxJjUbAzU+ZfAGZsjo7pYWKv36tXeyXHjuBqdvuwam1ZM3PZidriSyu/tT3TVdP5WddaxrS+wrKjuUKatRQSudPAYCAIlgD3io+As33osWsRhBP50yVg7ba46AaK4mM7YIAAEb6/F1beE4IghayEMtgOCzBW6WgW6MMhnwoFJmpSJ5acEFQK7qDP54vsoqYdD1yDfry1wp45WgTfUE5oLSwByW3akYo0wiUCBf9Y5l8UZ2zXiPQ7li5nd3IDq7ndZ98GD85slx3XLMcX0ngoo/dj6NLifqDdeTyRWTz5VpRJldQHfIZ1VxUhM/rQsDrKhOS/Psr1wgMTENZrhEYCAJTUUN5REzY6/uD1tpfVkMuL2F/EeOxSPfWGxKCoIXYnUPAGVTaSjbbxH49mUWf3wN3HdsqV/PrCZ54OlexeBBR1aYzyWwBkscFr7u069eGO6q2bsV/kNaYRUqCoKATBJXduarFyuv5pc89il/758eQd6hF4VceP4Er/+L7lp/HfRzZQqkst9ZpzM+FXLJDDrMtaQSl884XfX4+5UJ/tTQCnWnIoGeEEa3WCFZtLEGtZazPr5aR7zaEIGghC/G07aGjQKkva7ONPVZBTZEAACAASURBVNZTOTUipxa8VEC9pLLNjHFXqqBkvPNMZvPqbpYLAr1zM+Ct9B+kc0XVr5HJ19cIrFjQHn5pCXs++F3D+TYKYwxTt92DP/yPxvwRWY05iPsEskoyXbZQVM95Jl9UzxF3FqcNNQJ5fKjK95KoETVkNnzUjI/AatczI/KFItaTOYcEgVzyXR+C2w0IQdBC5jfsTSbjDCo2/WZ7F68nc3UdxYBWI6gvCMIGgkDuPmbslOR2aJ/HIGooV4Tfa2QaKqihgrJGUHpOvEYtfiuce/t9OK1UNW2GTL6AMz5wb/2BNVAFQZlGUMoy5t9PJl9QNSq/QUIZP39qHoFP9hHoM66rRQ1FFB9BPV9RvRLUnGjAi3Su2NRCu6aYluzqRaCFa/PdmF0sBEGLyBWKWElknDENhe2pN1SvFwGHmx7qagS6xvWcWhoBNz+4XASfx1WeNaxoBH6vfNlmckUwxpDJFzWCoIZG0IQgAIDL73gIX2giG/nQ6Q2c9cffa2oOgLFGkNEsoFGNaYgf83mNTEP68FFFwOraT3KhHdSFf4Z8ciXZWv0lgPpNaTh9NmQX29m0Xg8vHd+NDmMhCFrE8mYGjNkfOgqUNIJVG0xD9bKKgVIby7o+goyxIAhVs0VnC2W7Tr/XjbSurj7f2QKyaSNbKIKxkrkqnSuUhVBqFxUzjs16fPQ7L2Dqtnss1ymauu0evOlvftT0+wNQd/7ZfLmPgAtArWmIH/MpxQK5CQkwCB+tkvXNBbQ+Lj+sFp6rfl65VmLGR9BvobJtNZwoL8EZ6+IyE0IQtIhSDoH9pqGAJNt/V1tlGjKpEcjNTAw0girRKclMyUcAQLFpl4c78s8KlDuGuSYjL35a01DpfbI2On3P/KN7kTPxeoWi7A+wk7Qme7hQZCCSPxvf/fcZaATcRwCUdvwpvWmoSo7HZqZg+D2qpahrCAJ+/utFogHW26AaUSov4UDUkCoIhEYgaBB+8TihEQDNZxcXigyxdP3Ko0Bpx1lLhS8WmdyIvppGUKWmjTZW3e91VTiLy30EJdMI33Gmc3JmMc8rMJPw1Ch7P/hdPPDCQtXHF2Jp7P6j5vwBRnATF9+J6z9rNFDyEXChqD1vXBMwSiiTX9dYI9CjViCtcY7NVB7lcG20mXpDTpqGBoJeeN0kNIJqENGNRPQSER0hotsMHvcR0VeUxx8loinNYx9Qjr9ERDfYMZ9OZNHmFpV6BkNSU6YhOUGsfsE5APB5ZDt9reziUqRJ5QISlCob0wNK1JBmvN6mnVacxW4XwesmpPOFMhu4pPgUtCGUZsplN8Mt/3oQX/zpTMXxF+diuOwTDzr63vrOX1wwl0cNKc5ijyYkV1eYjh+vphEkMoWyEtQcLghqmYbMFJzj2KERrGxmQVQqQ2InRITRSHcmlTUtCIjIDeCzAN4A4FwA7yKic3XD3gNgjTG2B8CnITeqhzLunQD2A7gRwN8rr9d1LMQycLvIEZUVaF4j4Kn9ZgQBUL/eUEItIGccNWTkuE3qNIKAVB7uyJ3FAOD3uMtMQz6PC36PCxnFWcwXQyc1As6ffOtQmd/g6k99H2/46x86/r78HKoaGjfD+EuhtFrTkE9xspfCbuW8DW7757t+vfO3mkYQMmEaMlOCmtOvNKdppszEakLusOexOWmTM9rXnUlldlQfvRTAEcbYUQAgoi8DuAmANl/+JgAfVm5/DcDfkVx34CYAX2aMZQAcU1pZXgrgpzbMq6OYj6UxGvHVTdZqlKGQhFeWNht+Ps9BMGMaApSeBDV220a9CDhy1FCpOiYnmSlfcPhiz0kpzmIAat0cvemDm0OGFYEbd1gj0HKmA2agWsR1Cz//PqIBrSDg4aMlH4FqGlLaVHKqaQTJbMFwIY+YcBZbMQ1F/B4QNe8jcMIsxBmL+Jv6nXUqdojN7QC0pRJPKccMxyg9jjcADJl8blewEEurzS2coNmeBDy134yzGJBt8rWihvjiYGRSMOpHXCwyJDXlEQCuEchjtBmy8mMuJea8pBH4vC7Vb8CjiMwkPG1V9NVdS6ahkrOYC0qfpvqnWoxOo2EBtX0EoRoaQa2wXCumIZeLEPF5sNGEiXMlkXFM6wbkYA/hLG4jRHQrER0kooNLS0vtno5lFmMZjNlcbE7LYEhCMltoOBnHbo1AFQRVNAKgvOZPOl8AY9CFj5acxVoTB6A1DfGFzq0eyxaK6sLDWCk5rdtIVDMNBUoF+LQaQclZzKOOimWloWv5CPQF5wBzDeytmIYAnl3cuRrBaJ8fsXS+67KL7fiFzALYobk/qRwzHENEHgBRACsmnwsAYIzdyRg7wBg7MDIyYsO0W8tCPO1YxBBQ6sbUqFZQqjxqj4+glmnIaCep+hQknbNYrTBaypDlj2l9BDy/IJMvIpMrlJkizJgl7ODOd1+C5z/SungH3qOgtCCXawTaJDNt1VZtO0u/kUZg0kfg87jgdVNd05CLYKhRGNEfbK7e0GoiqyZYOkGpU1l3+QnsEASPA9hLRGcQkQTZ+Xu3bszdAG5Wbr8NwENMzku/G8A7laiiMwDsBfCYDXPqKNK5AtaTOUdyCDgDzQqCVA5EMJUBCtTvScCjhkIGUUMhdedZWQCtzFms2PwBlEUHAVC6bRXVapo8kokLB7/khuQuCQ1yxjWjMv2nb8D1+8cR9nlw9BNvhEOuIBXt64d1CX4Br/zZs4WimjPg12Rkcy0rky8g4C0tAX6PUhm2QhAUEDT4HomoquOfE0vJWcVk8guIBrwNh48WiwxryZytLSr1qLkEXRY51LQgUGz+7wNwH4AXAXyVMXaIiD5KRG9Rhn0ewJDiDH4/gNuU5x4C8FXIjuXvAfhtxlh36Vwo1SZx0kfAL/5GG9TIlUe9pp3Z9XoSbKrNTIwTygCUdcNKaNpUcrQagdYprD6mjRryuuDzlI753C7VJCR5XI6Zh37n6j049mdvLCst7nIRjv7Zm3Dnuy9x5D2BcoHN8wi4GcanfN6Mzoeir9HEE/S08w54y0N71cb1BqYhoH5PArN1hjjRgLnud0ZspHIoFJmzzuIuTSqzRWdmjN0L4F7dsds1t9MA3l7luX8K4E/tmEen4nQyGVDSCNaaMA1Zib3W9iQwsh/zJCPDonNcI9D4CFI5Y42A997VxsMDsiBYimfUhDK+412Iya/jU8Il4xlAcrsguV1lWcp28NDvX4kzR8JVH79+/zie+dD1uOAj/2nr+wLyAsxNKFzY8gXUr+RUZAsFZHIEyeMCEVUKglyhoq9vUJfsl9S1szSaR+2EshwiPvPXVX+w8S5lTpaX4HDTULcllXWnF63DmFcEwXgnawSpHKImHcVA/Z4EiUxlm0oO3/Ub+QjKwke9LhSZ3Hu3wlms+APSmqgYn9et2xXLY3mPAzv5r/9zVU0hwIkGvJj+0zfY+t5AuaYVVsNH5fMplWkEBVV48t2/tkSFX7fA65vTJNXvpUGNIGVNI+gPSFhPZi3XcgJK1XedjBrqD3oheVxqgmi3IARBC3CyzhCHm3VWG2xOs57MWtQIavck2MzkEZI8hrbhkEF0ipGPQFtcThv9AsiagbbAHDeH8F2yT2MOktwudR7VdrZWOPqJN2LXUMj0eK/bhZk73tT0+2rRalpajcDrJrhdBB8XlJrIIC4QVB9BrlghqPXNaZI1fD18HjUzi9PmehFw+oNeFJn55kFanCwvwSGirgwhFYKgBSzG0pA8rgo13E5cLsJA0IvVRGNqtdmCc5x6PQmqFZwDtD6CgmZ8pY+gtIMtlEW/yP/duuPusnr7kqIhAPJCzF0f1Xa2Zrhh/xhm7nhTRRVOs8zc8SZ86u0XNPz+kkarMYqKiqdzJS3ILVcaTedLkUEetxzlozUN6QVBSHKrZjqgsgyFnpCvdnMao3altVDLTDTgMObasBO9CLSMRfzCNCSwzoKSVWw2cqJR5DITjWsEZnMIgPoVSBO6ukFa+A5W65SsFjUkP1Yoi34BZCHBHcMuAjwuUpPNADmKiGsEXo8LLuXcV5tTPf75116Nf3r3gYaeq+UXLpnEj2+7uqHnah3eWtOQNo+glHntUvIIStnYgBwZlKriLAbk86rVCGrlgwCyo7perSFLpiHlGmwkcohrBAMWruNG6MaWlUIQtICFWMZR/wBnIChhrQGNIF8oIpbOm64zBNTvSbCZKRhGDAGlMEXtAsK1A+1CXap9k9c4i7WmoaJakVR2hpYu50rTEH9N6xrBE398LV5/1qjl51Vje38AL338RsvP83mNBYH2NtcIfB4lfFSXNOZXsrUZkx39fl00VUjy6Ex2tZ3FoRrO4mKRYTObt2Qaaqbw3Goii4jfA8nhBMLRPh8WNoQgEFjE6WQyzlBYaqiBPXcyWjIN1dMIapiGXC5C0Osuj07J5EGEsl19QFm0U9lK0xA3+8jmEOWY5rla05DkIXBdzKgaajUu3tmPVz7xRgyF7fft+DxuHPuzN+Iv3na+pedwyp3FWkFQCplNq87icgd8WSKeboEP+tw6H0F9Z3HCoL0lIJf3YMxaQp9airqB3sUriayjOQSc8T4/EtlC0x3vOgkhCFrAwkZrBEGjFUitlpcA6vckqCUIAN4ft1wjCHrLu2Bpq2FWJpTJ/9eTOU0kkcYE4tWYhsqcxeYWpT9649n4+m+91rEigYDseHz7gR342ntfY2p8mWnIwFkMaM6PR07GS+eLZZpEQOdbqfQR6L8XbrIzFqBq4TkD565aZ8jCBoNvRhozDWUcdRRzujGXQAgCh9nM5JHIFhyNGOIMKnVaChZD7/iPzoppqF5Pgs0qbSo5YZ8+OqWgagAcrY9AW0pC+389lSsLKeX4veWmIZdypZvxETzw/itw6xW7646ziwNTg3j+IzfULcOgDYHVmlt8Hje8bllgqedHkpPxMrmC7rzIPoJUFUEgd48r19SA6j6CWoXn9NVRzdDXhGloZTOLQQdDRzm8p0g3mYeEIHCYViSTcQZDEhiTHb9W2EhZ1wiA2vWGZI2g+sIWlNxlPgJ9Uxo+BpCTzdK5AohKkTN8AdtIak1DWh+BWzWleD0ucONQtQxZALhi3wie+ONrsWc0UnWMU4R9Hjz74RvwgTecXXWMNtZAa25xu0j9rGp1ViWCKm0gCNK5gpqx7dcLAq8HmXwReaUybKKOj6BWcxq14JwF0xAvl231GgZkH0GrTENAd5WZEILAYRYc7kymZVCxZVs1D3EHsxUfAVC7AmmiSp9bjtyusjyhTG+2CWpqEnFbNzfx8AVsI5WrMBfJt12qSUQbdlltTn/+tvPxhZsPOOIPMIvbRfiNK3fj73/5YsPHtVFn+nPFHaRcI+BZ2elcscwhLGsExYq8DA4XxklNZJGLqldwrVWBVF8W2yz9Qev1hhhjWEs6W3COM9qFTeyFIHCYlmoEwcYKz/GUfqthd9V6EmTzRWQLRYRr7L4rTBAGNe95aKPsLC7qfADcNJRVF6nyqCF3meOUm8v0C9/lu4fwj79yCX7xwA7HulpZ5Y3nTeAbv3U5PvKW/WXHtd4KbgrilM6BJrxWCbstE5AeFzJa05DeWawr/5HIVk8MBEq+CiPTUEzXQ9ks0YD1CqSxdB65AmuJRhD2eRD2eTDfRaah1tTn7WFKWcWtMQ0B1gXBRjKrVB61djn0BbyG71Uv9pw/dnI1WXpO1qjuTbmzuHxBK5VL4Md9msd9Xpe6S/Z5XCgqxfE8ivP3nIk+ZPIFfPIXzseOwaDJT9w6Lto5gPO2R/HAiwu4aEc//uahI2WCTh8iKekEAfcFFBkrex7Pv6jqLNYVBExmjCuPcmqahlRnsbXrKhqwXm+oFVnFWsb6fF3Vu7gztkBdzEIsre4gnGawwXpDa8kcogGv5YzZaj6CWr0IOCFd4lIyk0dQtyh5lWJxckJZeTy8T7fLBcrNF36vG1B85gHJrWoEY1FZIF+xbxgP/f5VHSkEOB63C198z2X4uQu2AQDOGi/5LvSCQK8V8f8Z3XnjzXuqCYKgJmQXkE1EtSKtapqG0o2bhqxmFq+2oOCclrG+7souFoLAYRZjmZb4BwCNINi0bhpqJBuzWk+CUi+CGqahCh+BcbipbOKQncXahT5gIBTKBIXHpTZukdyl21ftG8E/vfsS/O/rzzL1GTuBvWMRfO6/H8Dtby6ZivQ2e0mXSxHQOYg53GSU0uVlcLgWxnf4+j7SemppBBupHCI+j+UQ3P6AZDmPgF/zwy3y8Yz1+bvKNCQEgcMsxNIYizhvFgKg1jOymlS2nsw2VAepWk+Ckmmo9gLCG9gDPNy0cjxvdJ/Kljufy8smKLtgbUKZu+QXcBHhHa+WG+GNRHy4Yf+47dVInebac8cQkNxVM6TVqCFvpSAoi6byupDOF0tVRX16B33JHAfIQr2WIKgVPipXHrV+XTXiLG61aWhUMQ1V68ex1RA+AoeZj6Xx6qnBlr3fUFiyrhEkcw0V6qrWk4CbCWqZhoI+2VyTyRfh87iQyBpHGQUkN5K5AhLZ8rwEfUgkUF6CgYiQL8qRMR434Xev3ou3XzJZ4Szeajz6gWvg1Wg4HL7rVqOGNIu3vn5TNl9UzTZ6hz7/Dri2tpnJY6TGLlvyyL4Yo8JzsXSuoTah0aBXqZxaMP19rbRYEIz3+ZEryB3RWvWeTtLUtoiIBonofiKaVv4PVBl3szJmmohuVo4FiegeIjpMRIeI6I5m5tKJMMZaahoCgOGQD8ub1jSCtWS2MdNQlZ4E3PZv1JSGw+P5E5k8MvkiCkVWtdF9KluQTUcGJaqB0uKlXzQmogEAwLZoAAHJbap/QKcz2ufHQEhSFx++W88pcf/8O9GeC+33wI8vK5uFarkbXGPYTOfVfgfVqFZ4Ti44Z10jiDaQXbyayCIkuVsm6Lstu7hZ/fg2AA8yxvYCeFC5XwYRDQL4EIDLAFwK4EMagfGXjLGzAVwE4LVEZH8HjzaynswhWyi2zDQE8HpD1jUCK1nFnGo9CUqJRNVfU2uCqOVcDnrlkgf6vAStaYjvOvUF1H75sp24/c3n4op9I6Y/01bB7SL81S9egG//zusAlKKh+CKqNQ1pTW78+MpmBj6PqyJkVt8rQi4jXXtXX63w3EYq15DJsT8gqc83i9NN6/XwSgHzQhAAAG4CcJdy+y4AbzUYcwOA+xljq4yxNQD3A7iRMZZkjD0MAIyxLIAnAUw2OZ+OgmcetiJ0lDMctqYRZPNFbGbyTWoE5T/YeLp+jZmwxgRRK9yUOzf1mcd+gwJsPt1usD8o4ddfd4bj1SjbxX+7eBK7FS3Ho9TQUIVimSAofQ9cgC5vZur0k5Y1gnimviCo1qUsnrZWeZSjFp6zkF28kmhNeQkO/013S6eyZn8hY4yxOeX2PIAxgzHbAZzU3D+lHFMhon4APwdZqzCEiG4looNEdHBpaam5WbcIHl42Hm3dBToUlrCezKmmgnrw6Awr3ck41SqQxlJym8patXOCarSJViOo7izWZx5rQ125AOG73d0j5ruHdQuvnpKV7G39sjlMKzTLBKjGNGQkeCW3C24XIZnNI5MvIJsvIlIn9LmaILDai4CjmoYsaQSZliSTcUa6rHdx3W+JiB4AMG7w0Ae1dxhjjIgsu9CJyAPgSwD+hjF2tNo4xtidAO4EgAMHDmwJVz0vSjXaUtOQfIGuJbJqKnwtSgXnGtEIjHsSyE5Cb81GPCFNmGKhKN+uphHE0rKJrVoJab6zdbsId7/vtS3p/dBp/MaVu3HxrgHs39YHoLxvr1HvgvlY2jDUkoiUOlAF1elfLw8g7PdUJFcVigzxTL4x01DQepey1c0szh7vs/xejeLzuDEYkrrGNFRXEDDGrq32GBEtENEEY2yOiCYALBoMmwVwleb+JIDva+7fCWCaMfYZUzPeQrSyzhBnWNkVLW+aEwRrTXR1qqYRxNP1G5bzRT+ZzathnkaCoM/vVXdd1RKbtIvN+ZP9JmffXYR8HlylaZ4zECqdE239JL7ILsUzmBoyTqbjpag3VUFQXyM4tlwoOxY34SeqhtqlzGQuAWOsZb0ItIz1+YVpSOFuADcrt28G8C2DMfcBuJ6IBhQn8fXKMRDRxwFEAfxek/PoSBbiaQwEvWUNRZxmWFFZzeYSrCm7Lu3CYZZqPQliqRwivjq7SN5wPZ0vJaAZLPRaAVUtL2E82nsaQD2qNbHRCs1aPaWT2YKpMGD+OvrMYq4lNhI1FJLccLvIdNQQL1Pe6jBOuYl9d5iGmhUEdwC4joimAVyr3AcRHSCizwEAY2wVwMcAPK78fZQxtkpEk5DNS+cCeJKIniaiW5qcT0exEMu01FEMQN0Vmc0l4A65RjSCaj0JzGgE0WDJ0VwrAW1QI6D05qv3XrkbIxEfJgcClufeC7z+rBFcqsthiQZK57Dady5rBAXEM+ZKRET8HmxmqkWOWfcREBH6LRSe49d6ywVBxN87pqFaMMZWAFxjcPwggFs0978A4Au6MadQXlCx61iMtaYzmRZuBjAbOaRqBA02/DaqNxRL5+rW8OGlB7S7PiMtQrv463/of3DDWfif1+zdclnCreKf3n0A+uoOWo2g2nceUHpFxE2ahkKSB+mc3MOAh6PyRbwRHwEgbxTMOou59ttIUmQzjPXJEXraz71V2dqz73DmY+mWdCbT0uf3wOsmNWGoHmtJuYyzvhyx6fcz6ElgJmyQ7/rWU1nEUrmq1U+1i5V+4XK5qOF59wKSQZ6A5HGpWcjVFs6QEqll2kfA21Vqigg20qZSS3/AfOE5fq2PhFu76RqL+sEYTP/WOhkhCByiUGRYirfeNEREGAr5sGJWI0g0llXMMepJYDZsMBr0Yi2Zw3qqevVTbaJbN6TydwLcOV/tfAZ9ckHAdZO7+ojq7ykt3GafW43+oPnCc0tx+VofjrTeNAR0R1KZEAQOsbKZQZG1NpmMMxwxn1281mBWMUevERSLDJvZvKnSw3zXt57MVe2OtlMT2dJIroOgEu783VnFfBdSkvjWElm4XVRXu1PDPTWmnGaLwPUHzBee42bQoRYmlAHdVWZCCAKHaGVDGj1WNIL1ZLapnbbeRxDP5MGYOSch3/WtJbOIVtFK+vxenLc9iqvOGqmZlyAwz61XnImg5FZzDvQEJbl20Eoii4Fg/T4VA8r1s6bJBF5LZBFsovZP1EIF0qV4BgNBb8szyMeURNFuCCEV1UcdotSisvU9cIfCEo4sbpoau5ZsLhFH35NAtQ2b1AheXojDRVRTGP37e18DlxACtvE7V+/BLT97RtW8jJDPjUS2gNVExtQmgWtqa5qFe7XBQoacoZCEzYyc3Vwv/HopnmlZHwItQyEf3C7qihBSoRE4xHwLexXr4fWGzNRKb7TgHEffk2BdzUuovwjwXV8t0xAgl0Xo1npB7UDOHq6+BxwISigUGY4tJ0wt5moCmE4jaEbT5HWDzLRdXd7MqCUfWonbRRgJ+4SPQFCdhVgaLkLLsx0BYDgsIZMvqoXDqsEYa7g7GUfbkwCQd4JAefx/Ncb7/NjM5HFiNdmWHZ3AGF6+++WFTVMhmVyIryW0GkHO1GagGvx9zeTDLLVJEABy5JDwEQiqcnpdziFoR3wxd5rV8xPE0nJ5h2Y1AqCUSWqlZMXkQMlZOdEvksI6BW2RRC4UauFxuxDxeyp8BINNXFdDFvpvt8s0BABjER8WhWlIUI35WAoTbSp9wHdT9eKbm8kq5uh7EljpFKXNCN4mykR0DOOaxb9aZJGegaBUZhpabbIsNE+MrLeZSWTySGYL7dMI+roju1gIAoeYW0+3bZc7bDK7mAuKZjIy9T0JzIYcAijLPj6jB0tHdypjmkV1atjc9zKg5IQAQCYvlxY3Yx6sBr8m6/kI+DVeq52mk4z1+bCRyiGdq22G7XSEIHAAxhjmNtKYaFM5ZF7ttF5YG/8RNaNW84QhvgjI0SL1Qw4BWWu4YDKKgaAXe7qgjWS34HG7cM3ZowhKbly001w1136NRtBMaXNOxGcuQ76UTNYeQcC1p7mNra0ViPBRB9hI5ZDKFdqmEZgNa7NDEHChwx1mVjOV//XXL0O2C2q1dBt/90sXI57OmS4jPRD04thyAgBUm/loE4szz5BfrVNFlwuCdmkE3KQ5t57CGSa1p05ECAIH4LuDdvkI3C7CaKR+WNtyvHnT0EjYBxeVBMFKImspWiQqsoU7koDktlTHaSjsw1JcDlm2K3R6MCTVjRpSNzMtLi/B4R3hTm9xjUBswxxgbiMFoH2CAABG++qHta0kMugPepuq3ulxuzAS8WFe+SG0o+KqoP1MRP1I5QqIpfOqIGi2T8RQWMJyHR/BUjyjhGm3yzRU0gi2MkIQOMDpda4RtC8kciziqysIljft6fM6Hg1gPpYu+UZEBFDPwRfE+Y00FjbScLuo6ZDOoZBU1zS0GM9gUDGFtgO/142hkITTGz0sCIhokIjuJ6Jp5f9AlXE3K2Omiehmg8fvJqLnm5lLJzGv/BDaFdIGyD/Muj6CeNaW+OvxPlkjWEvmkMkXe7JncK/Dv/O5jRTmY2mMhJtfnIfCvrqmoflY+zceE/1+dfO3VWlWI7gNwIOMsb0AHlTul0FEgwA+BOAyAJcC+JBWYBDRfwNgrjDOFuH0RgpjkfbtUgDZPlsvrG15M2NLtMVENID5jXRHmMQE7UGrEZxeT9nSPnQoLCGZLSBVI0N+fiPd9lalE9GAeu1vVZoVBDcBuEu5fReAtxqMuQHA/YyxVcbYGoD7AdwIAEQUBvB+AB9vch4dxfxG+3IIOGZK5C5tZmyJtpgcCCCeyePZUxsARJZwLzIa8YMIOL2ewtGlBM60IS+klF1cXbPtBFPk9v4A5npcIxhjjM0pt+cBjBmM2Q7gpOb+KeUYIPcy/hSAZL03IqJbieggER1cWlpqYsrOM9cBuxRe9XS+SjRDJi83J7fDR3DWeAQAcO9z8qWwWySH9RySgzkaUAAAGHpJREFUx4WpoRCeOrmO+Vgau23ICyklRhqbh5LZPDZSubb/1iaifsQz+YpOfVuJuoKAiB4goucN/m7SjmNy+cn65S5Lr3shgN2MsW+YGc8Yu5MxdoAxdmBkZMTs27Qc2WGaanvJBG6zXYgb76a47dUO09BZY7Ig+OH0MiaiflNNaQTdxzkTEfxwehkAsGe0eUHAtdpqmxl+vN0+Ka4Bb2WtoK4gYIxdyxh7lcHftwAsENEEACj/Fw1eYhbADs39SeXYawAcIKIZAD8CsI+Ivt/cx2k/68kc0rliWyOGADl8FKieXaxmZNpgGhqJ+FTBd/FOw3gBQQ9w3vZSFvIlu5q/DuqZN1VB0OZNF7/2t3LkULOmobsB8CigmwF8y2DMfQCuJ6IBxUl8PYD7GGP/wBjbxhibAvA6AC8zxq5qcj5t53SHOEz7/B4EvO7qu6mYfUlvRIRfumwniIC3HZhs+vUEW5ObLtyGsM+D684ds2WDMRSS4HVT1cTI0jXc3k1XN2gEzWYW3wHgq0T0HgDHAfwiABDRAQDvZYzdwhhbJaKPAXhcec5HGWOrTb5vx8IX3nY7TIkI41F/1RooPAHGrt3Ub79+D37psl2iwXwPs60/gB/fdjVCFjKSa+FyEUYj/qqbmbkOMQ2NReTs+q0cOdSUIGCMrQC4xuD4QQC3aO5/AcAXarzODIBXNTOXTuF0m8tLaJkcCODUmrEffi6WhuR2YbCJwmBaqE67SUFvEK3Raa4RxqPVBcH8Rhr9Qa+lUhhO4HG7MNbnx+wWzi4WmcU2M7eegseGrEo7mBwI4uSa8cXJ46/NVAkVCNrFeI1SKbPrqbabhTgTUf+WNg0JQWAzs+spTPT725pMxtkxGMBqIotEJl/xWCeEuAoE9eCNX4z6b59YTWKXycY5TjPRv7WTyoQgsJnZtRQm+zvj4tyhtII8aWAemu+ARByBoB7jUR+S2QLius1MschwcjWJnUOd8VvbpvjjjATWVkAIAps5tZbC9oHOUFd5B7CTq+U7lWKRdURqvkBQj2q5BEubGWTyxbIud+1kIhpAJl+s21GtUxGCwEYy+QIW4umyXrztZIcyj5Or5RrB8mYG2UIR2zrEvioQVGOnupkpv4ZPKPfN9lR2GrUvwRb1EwhBYCNz62kwJjtpO4HBkISg5K4wDc2syPfN9qMVCNrF1JB8jfLuZ5wTK50lCLYrgmB2vW61nI5ECAIbOaVE6HSKRkBE2DkYxIzuRzSzIt+f6hD7qkBQjf6gF31+D46vlC+wx1eTcFFpAW43Owa59r01HcZCENgI3w10ysUJAPvGInh5obzK9/GVBDwu6qh5CgRGEBGmhkPq5oVzZDGOnYNBSJ7OWMKiAS8iPo9hYMZWoDPOYpdwai0Ft4s6Khpn31gYs+spbGqiLmZWkpgcCIiG8YItwdRQqEIjeGk+jn1KscNOgIgwORis8GVsFcRKYCOn1lIY7/N31ALLfyzTC3H12NGlhPAPCLYMU0NBnFpLIpOXG9Rk8gXMrCTV8uedws7BQNUEzk6nc1asLuDUWrJj/AMc/mN5WREE2XwRRxbjOGeir53TEghMs288giIDphUT59GlBApFhr0dpBEAct7OydXklswl6ClB8D/+9SA+/p0XHHv9Tsoh4OwYCCIkufHcrNw9bHoxjlyB4VwhCARbhPO2RwFA7YD3zMl1AOi4a3jHYBCZfFEt8W43Xz14Em/+2x9iI2V/A5yeEgSxVA5PnFhz5LWz+SLmY+mOCR3luFyEi3cN4PFj8ud+XhEI+7d11o9IIKjGzsEg+vwedTNz8PgaBoLejuuEp0YOOeQwPjS7gZnlJPr8zRaNrqSnBMG+sQiOLGw6orrNb/Acgs7SCADgZ84cwksLcawmsvjJKysYDvtwhvARCLYIRIQLdw7gsWMrYIzhsWOruGTXAIjaX89Li1rSxaEQ0unFTewZDTvyuXtMEIQRz+Sr1uhvBr4LmOzAkMzX7hkGANzz3Bx+OL2M1+0Z6rgfkUBQi6vPGsErSwnc+9w8Tqwm8fqzR9s9pQomB4yzoO1ienETe21oAWpETwkC7lx6WRNBYxc8vG1XB+60L5iMYt9YGH/yzeexmsjirRdtb/eUBAJL3PCqcXjdhN/+/5+E3+vCjfvH2z2lCgKSG8NhnyOmofVkFkvxDPaOdaAgIKJBIrqfiKaV/4aNSonoZmXMNBHdrDkuEdGdRPQyER0mol9oZj71KIVSbtYZaZ3jKwlIHhcm2twtyQgiwoffsh/9QS/efP4Ertg70u4pCQSWmIgG8P7rzkJQcuO2G8/GUAf0+zBix2DAEdPQkUV5zdo76kykVLNeh9sAPMgYu4OIblPu/6F2ABENAvgQgAMAGIAniOhuxtgagA8CWGSM7SMiF4DBJudTk8GQhOGw5IhGMLOSwM7BYMc2erl89zCevv36dk9DIGiY37xqN9575ZkdbdbcMRDEkw4EpEwrgmBPh5qGbgJwl3L7LgBvNRhzA4D7GWOryuJ/P4Ablcd+HcCfAQBjrMgYW25yPnXZOxrBy4tOaARJUbtHIHCYThYCgKwRzG2kkS8UbX3d6YVNBLxux8rCNCsIxhhjc8rteQBjBmO2AzipuX8KwHYi6lfuf4yIniSifycio+cDAIjoViI6SEQHl5aWGp7wvrEwjizEbY0cYoxhZiWBXUOd5x8QCAStY9dgCIUiUwtQ2sX0Yhy7R0OOWRzqCgIieoCInjf4u0k7jskrq5XV1QNgEsBPGGMXA/gpgL+sNpgxdidj7ABj7MDISOM27r1jESSyBVsbTS/GM0jnikIjEAh6nDOU3IZjuiJ5zXJ4Po6zx53L/anrI2CMXVvtMSJaIKIJxtgcEU0AWDQYNgvgKs39SQDfB7ACIAng68rxfwfwHnPTbhytw9iu5C9eK11oBAJBb3OmEjV4dCmB159lz2uubGawFM/gbAdrKzVrGrobAI8CuhnAtwzG3AfgeiIaUKKKrgdwn6JBfBslIXENAOfqPyjsU8Kv7HQYH1fr+wtBIBD0MoMhCX1+D44t2+eHfGleXqucrA/WrCC4A8B1RDQN4FrlPojoABF9DgAYY6sAPgbgceXvo8oxQI4w+jARPQvg3QB+v8n51KU/KGE04quo0d8MMytJeFyEbf2dFzoqEAhaBxHhjJFwRUe1ZnhREQROVlttKnyUMbYCeSevP34QwC2a+18A8AWDcccBXNHMHBpBbtZir0awczDYUeWnBQJBezhzOIRHj67Y9nqH52IYDvsw7GDuRE+uXOdMRPDSQhw5m0K8ji0nsVM4igUCAWRBcHojjVS2YMvrHZ6P45wJZ0tu96Qg2L8timy+iFeWmjcPFYoMR5c2sXvEmUQPgUCwtVAjh2wwD+ULRby8EHfUUQz0rCCQnS4vnI41/Vqzaylk8kXHikEJBIKtBa/sa4cgmFlJIpMvOho6CvSoIDhjOASfx4VDNgiCI0uyr8GpYlACgWBrURIEzVscDs/La9TZwjRkPx63C2dP9OHQ6Y2mX4sXsNsz0llt8wQCQXsISh5MRP04utS8RvDiXAxuFzlWY4jTk4IAkM1DL5yONV1qYnpxEyMRH6JBr00zEwgEW509o2G1UFwzPD8bw76xCHwetw2zqk5PC4JYOt90TZAjDjaLEAgEWxMeol4oNr7RZIzh2VPrOF/p2ewkPSsIeOPrZvwEjDEcUdrHCQQCAefs8Qgy+aJadaARTq2lsJbM4bxJIQgc4+zxPrgIeKEJP8FCLIPNTF5oBAKBoAwe5cPLQzTCc7Py2nS+EATOEZDc2DsawTOnGhcE3KPPW2AKBAIBIEcRukhOBmuUZ09twOsmR0tLcHpWEADARTv78fTJdRQbtONxs9K525yN8RUIBFsLv9eNqaFQkxrBOs4e73PcUQz0uCC4eOcANlK5hmuHv3A6hh2DAfT5RcSQQCAo56xxuZRNI8iO4o2W+AeAHhcEF+2Um6Q9ebyxHqMvzMWwf6I1X5RAINhanDUewcxKoqGaQ0eXE4in87hACALn2T0SRsTvwZMn1i0/dzOTx7HlhDALCQQCQ86Z6ANj8obRKgdn5Er9B6YG7Z6WIT0tCFwuwoU7+vHUCesawWHly90vBIFAIDDgwh2yxeGZk9Y3mo/PrGEwJKkdz5ymKUFARINEdD8RTSv/B6qMu1kZM01EN2uOv4uIniOiZ4noe0Q03Mx8GuHinQN4eSGOzUze0vOeV0K7hEYgEAiMGOvzY7zPj2dOWRcEB2dWcWDXAIicaVavp1mN4DYADzLG9gJ4ULlfBhENAvgQgMsAXArgQ0rbSg+AvwbwesbY+QCeBfC+JudjmUt2DaDIrPsJnjq5jrE+H8b7RFcygUBgzAU7opY1gsV4GjMrSby6RWYhoHlBcBOAu5TbdwF4q8GYGwDczxhbZYytAbgfwI0ASPkLkSz2+gCcbnI+ljkwNQCvm/DjV5YtPe+J42u4pIUSWyAQbD0u3DGAmZUk1pNZ0895YkbelB6YMjSwOEKzgmCMMTan3J4HMGYwZjuAk5r7pwBsZ4zlAPwmgOcgC4BzAXy+2hsR0a1EdJCIDi4tLTU57RJByYOLdgzgJ0fMt5ZbiKVxai2Fi3e27osSCARbjwt2yFE/T1vQCn56dAUBrxv7t7UuIrGuICCiB4joeYO/m7TjmFzG03RmFhF5IQuCiwBsg2wa+kC18YyxOxljBxhjB0ZGRsy+jSku3zOE509vmJba3Ix0yS4hCAQCQXXOn+yH20U4OGPe9PyDl5fwmt1DkDyti+Wp+06MsWsZY68y+PsWgAUimgAA5f+iwUvMAtihuT+pHLtQef1XFCHyVQCXN/l5GuK1e4bBGPDI0VVT4x+fWYPkcbVUYgsEgq1H2OfB+ZNR/MSk6fnEShIzK0lcsbe1cTPNipy7AfAooJsBfMtgzH0ArlccxAMArleOzQI4l4j49v46AC82OZ+GuGCyH0HJjR9MmzM5/fjIMl49NdBSiS0QCLYml+8ewjOnNkxFJv7wiLwG/ew+e60e9Wh2JbsDwHVENA3gWuU+iOgAEX0OABhjqwA+BuBx5e+jiuP4NICPAPgBET0LWUP4RJPzaQjJ48KV+0bwwAsLdesOLcTSeGkhjiv2tvaLEggEW5PLdw+jUGR47Fh9P+TDh5ewvT/QsvwBTlOCgDG2whi7hjG2VzEhrSrHDzLGbtGM+wJjbI/y98+a4//IGDuHMXY+Y+znGGPmPbY2c+OrxrEYz+CpOk6dH07LKt7PCkEgEAhMcMku2XrA145qxNM5/GB6CdfvH2t5NKKwbSi8/uxReN2E+w7N1xz38OFFjER8OLsFpWEFAsHWx+9142f3DOM/Dy3UbI370OFFZPNFvPG8iRbOTkYIAoU+vxev3TOM7zxzump7uUQmjwcPL+DG/eNwuUT+gEAgMMeNrxrH7HpKbTZjxHeencNYnw+XtCEsXQgCDb94YAdOb6SrOo0fPLyIdK6IN5/feoktEAi2LtedOwaPi3DPs3OGjy/E0njo8CJuunB7WzaZQhBouPacMQyHJfzfR04YPv6lR09ge3+gpanfAoFg69MflHD12aP49ydOIZ2rLEv95cdOolBk+KVLd7ZhdkIQlCF5XHjXpTvxwIsLeEHX1P6F0zH89OgK3v2aXcIsJBAILPOrl09hNZHF3U+XV9KJp3P4l58cw+vPGsFUi6OFOEIQ6LjldWeiz+/Bn333RdWxwxjDHd87jD6/B+989Y46ryAQCASVvGb3EF61vQ+feeDlsmY1n334Fawlc3j/dWe1bW5CEOiIBr34PzechR9OL+MzD0yDMYbP/fAYfvDyEn7v2n3oD0rtnqJAINiCEBFuf/N+nN5I4wNffxa5QhH/eWged/7gFbz9ksmWtaU0wtO2d+5gfuVnduGpE+v46wencddPZ7CezOGG/WP41cun2j01gUCwhbn0jEH8/nX78Kn7X8bDLy1hI5XD+ZNRfOgt+9s6LyEIDCAi/OXbL8DPnDmER46u4MKd/fjly4RvQCAQNM/vXLMXZ41H8J8vLODMkRB+9fIpBKX2LsVUK8GhUzlw4AA7ePBgu6chEAgEWwoieoIxdkB/XPgIBAKBoMcRgkAgEAh6HCEIBAKBoMcRgkAgEAh6HCEIBAKBoMcRgkAgEAh6HCEIBAKBoMcRgkAgEAh6nC2ZUEZESwCON/j0YQC1e8a1BzEva4h5WUPMyxrdOq9djLGKPrtbUhA0AxEdNMqsazdiXtYQ87KGmJc1em1ewjQkEAgEPY4QBAKBQNDj9KIguLPdE6iCmJc1xLysIeZljZ6aV8/5CAQCgUBQTi9qBAKBQCDQIASBQCAQ9DhdIwiIaJCI7ieiaeX/QJVx3yOidSL6ju74GUT0KBEdIaKvEJGkHPcp948oj085NK+blTHTRHSzcixCRE9r/paJ6DPKY79KREuax25p1byU498nopc07z+qHG/n+QoS0T1EdJiIDhHRHZrxDZ0vIrpR+ZxHiOg2g8erfl4i+oBy/CUiusHsazo5LyK6joieIKLnlP9Xa55j+J22aF5TRJTSvPc/ap5ziTLfI0T0N0RkuVVgE/P6Zd1vsEhEFyqPteJ8XUFETxJRnojepnus2m/T+vlijHXFH4A/B3Cbcvs2AJ+sMu6a/9fOuYXWUYRx/PeZ2HhBbeql1qbSBFpKvSFG7YsSq6QqthVSNEWsFwTRJ9+rLyKIbyp96ENBmgdbNaJGRaStrRShKGnT0CLanCiYY7xQb6WViPj5MN/KuOzJ2d2c3aQ584dDZr+d75v//ufMzM4lB1gPfBCzvwn0W3o78JSlnwa2W7ofeKPRvIBFwLj9bbd0e0K+YeB2Sz8KbCtSr+l4AQeA7gSfWdMLuAC4w/IsAA4C9+TVC2gBKkCXxTsKrE7zvMBqy98GdFqcljQxC+Z1I3CVpa8Fqp5PYp2WxGs5cKxG3M+BNYAAH0V1WgavWJ7rgErJei0HrgcGgE0p22ZmvebNjADYCOy09E7g/qRMqroPOOXbbMRcCwwm+PtxB4E7M76RpOG1Dtijqr+o6q/AHuDuGMeVwBW4zq0RaAivOnFL1UtVz6jqfgBV/Qs4DHRkKDuOW4AxVR23eLuNXy2+/vNuBHar6pSqfgOMWbw0MQvjpapHVPV7sx8HzheRtozlN5xXrYAisgS4WFUPqevlBqjRtkvgtdl8G4W6vFT1W1UdBf6J+Sa2gbx6zaeBYLGqTlr6B2BxBt9Lgd9U9W+7ngCWWnop8B2A3f/d8jeS139lJJQfIXpL8Y959YnIqIgMisiyDJwaxes1mxI/5zWaOaGXiCzEzfz2eeaseqWpl1rPW8s3TcwiefnoAw6r6pRnS6rTsnh1isgREflURG7z8k/UiVk0rwgPArtitqL1yuqbS6/WlIXOCYjIXuDKhFtb/QtVVREp7VxsSbz6gYe96/eBXao6JSJP4t5m1voOBfN6SFWrInIR8LZxG0jjWLReItKKa7Cvquq4mevq1UwQkWuAl4Bez5y7ThuASeBqVT0pIjcB7xrHOQERuRU4o6rHPPNs6tVQnFUDgareVeueiPwoIktUddKmRz9lCH0SWCgirfY20AFU7V4VWAZMWAdzieVvJK8q0ONdd+DWH6MYNwCtqjrslelz2IFbW/8fiuSlqlX7e0pEXsdNcweYA3rh/unmhKq+7JVZV68a5fgzB/97Ec8Tf97pfOvFLJIXItIBvANsUdVK5DBNnRbOy2a6U1b+sIhUgJWW31/eK10vQz+x2UBJek3n2xPzPUBOvebT0tAQEO2cPwK8l9bRvoT7gWhX3vf3424CPoktzzSC18dAr4i0izsl02u2CJuJfQmtk4ywAfgyA6cZ8RKRVhG5zHicC9wHRG9Ks6qXiLyAa8TP+A459foCWCHuRNkCXGcwNA1f/3mHgH5xp1E6gRW4Tbw0MQvjZUtmH+I25D+LMtep0zJ4XS4iLVZ+F06vcVsm/ENE1tjSyxYytO2Z8jI+5wAP4O0PlKhXLSS2gdx61dtNPls+uPW8fcAJYC+wyOzdwA4v30HgZ+BP3PrZOrN34RrqGPAW0Gb28+x6zO53FcTrcStjDHgsFmMcWBWzvYjb7DuKG8RWlcULuBB3gmnUOLwCtMy2Xri3H8V18iP2eWImegH3Al/jTndsNdvzwIZ6z4tb6qoAX+Gd3EiKmeP7nosX8Cxw2tNnBHcIoWadlsSrz8odwW3yr/diduM62QqwDftFhDJ42b0e4FAsXll63Yzrp07jZijH6/UZefQKPzEREBAQ0OSYT0tDAQEBAQE5EAaCgICAgCZHGAgCAgICmhxhIAgICAhocoSBICAgIKDJEQaCgICAgCZHGAgCAgICmhz/AmWIHp0y4ysfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (2) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(-0.1,0.1,10000)\n",
    "y = x*sin(1/x)\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fed140a3690>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (3) TYPE YOUR CODE:\n",
    "\n",
    "x = linspace(-0.1,0.1,10000)\n",
    "y = x*sin(1/x)\n",
    "plot(x,y)\n",
    "\n",
    "y = abs(x)\n",
    "plot(x,y)\n",
    "\n",
    "y = -abs(x)\n",
    "plot(x,y)\n",
    "\n",
    "# (4) RECORD YOUR ANSWER: the limit is 0\n",
    "# (5) RECORD YOUR ANSWER: The squeeze theorem"
   ]
  }
 ],
 "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"
  },
  "title": "yournamehere"
 },
 "nbformat": 4,
 "nbformat_minor": 4
}