{
"cells": [
{
"cell_type": "markdown",
"id": "8cffc5b0",
"metadata": {},
"source": [
"# Limits and Derivatives\n",
"**Instructor:** Isidora Rojas (i1rojas@ucsd.edu)\n",
"\n",
"**TAs:** Joey Carter (j6carter@ucsd.edu) and Lauren Harvey (lrharvey@ucsd.edu)"
]
},
{
"cell_type": "markdown",
"id": "e7314f0f",
"metadata": {},
"source": [
"## Learning Objectives\n",
"- Explain a limit and use it to define the derivative\n",
"- Compute derivatives using power, product, quotient, and chain rule\n",
"- Understand and identify different forms of differnetiation notation \n",
"- Apply derivative rules to oceanographic problems"
]
},
{
"cell_type": "markdown",
"id": "d13df1b4",
"metadata": {},
"source": [
"## 1 | Limits"
]
},
{
"cell_type": "markdown",
"id": "d97f0c92",
"metadata": {},
"source": [
"
\n"
]
},
{
"cell_type": "markdown",
"id": "222e0f44",
"metadata": {},
"source": [
"\n",
"We say that the limit of $ f(x) $ is $L$ as $x$ approaches $a$ and write this as:\n",
"\n",
"$$\\lim_{x \\to a} f(x) = L$$\n",
"\n",
"This means we can make $f(x)$ as close to $L$ as we want for all $x$ sufficiently close to $a$, from both sides, without actually letting $x$ be $a$.\n",
"\n",
"**Simple Example:**\n",
"\n",
"$$\\lim_{x \\to 10} \\frac{x}{2} = 5$$"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b5bf9d06",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import sympy as sp\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "ec770f43",
"metadata": {},
"outputs": [
{
"data": {
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d3ZWHH35YOXny5B1fQ4jyplKU265wJoQQVdjMmTOZNWsWV65cMR4DU5yAgABatGjB5s2bKyk7IYSlkGOAhBBCCGFzpAESQgghhM2RKTAhhBBC2BzZAySEEEIImyMNkBBCCCFsjjRAQgghhLA5ciHEIhgMBi5duoSbm5vcnE8IIYSoIhRFIT09HV9fX+zsSt7HIw1QES5duoSfn5+50xBCCCHEXbhw4cIdbyosDVAR3NzcgJs/QHd393IdW6fTsXXrVvr27YtGoynXsS2BtdcH1l+jNdeXmZeJ73u+AJybeA5PF0/zJlRBrHkbgtRnDSqqxrS0NPz8/Ix/x0siDVARCqa93N3dK6QBcnZ2xt3d3Srf2NZeH1h/jdZcnzpPDf/ccNzd3R13l/L9/bYU1rwNQeqzBhVdY2kOX5GDoIUQQghhc6QBEkIIIYTNkSkwIYTNsLezZ3TQaC5evIi9nXz8CWHL5BPgHuj1enQ6XZnW0el02Nvbk5OTg16vr6DMzMca69NoNKjVanOnIcqB1l7LqsGriIyMRGuvNXc6QggzkgboLiiKQlJSEjdu3Lirdb29vblw4YJVXmPIWuvz9PTE29vbqmoSQghbJg3QXShofmrVqoWzs3OZ/igaDAYyMjJwdXW940WaqiJrq09RFLKyskhOTgbAx8fHzBmJe6EoCpl5meToc5D7QAth26QBKiO9Xm9sfmrUqFHm9Q0GA3l5eTg6OlpFg3A7a6zPyckJgOTkZGrVqmXmbMS9yNJlUW1hNQCu97uOg4ODmTMSQpiLdfyFqkQFx/w4OzubORNRmQq2d1mP+RJCCGGZpAG6S3IsiG2R7S2EENZFGiAhhBBC2ByzN0AJCQk88cQT1KhRA2dnZ1q3bs3ff/9d4jo7d+6kbdu2ODo60qBBA1auXFkoZv369TRr1gytVkuzZs3YuHFjRZUghBBCiCrGrA3Q9evX6dq1KxqNhi1btnDkyBHee+89PD09i13nzJkzDBgwgG7duhETE8OMGTOYOHEi69evN8bs2bOHESNGMHr0aOLi4hg9ejTDhw9n3759lVCVEEIIISydWRugBQsW4Ofnx+rVq+nQoQMBAQH07t2bhg0bFrvOypUrqVevHkuWLKFp06Y888wzPP300yxcuNAYs2TJEkJCQggLCyMwMJCwsDB69+7NkiVLKqGqqmHFihUEBARgb2/Ps88+S61atTh79myp1x82bBiLFi2quASFEEJYrZjzN8gw8zklZj0N/vvvv6dfv3489thj7Ny5kzp16vDCCy/w7LPPFrvOnj176Nu3r8myfv36sWrVKnQ6HRqNhj179vDSSy8ViimuAcrNzSU3N9f4OC0tDbh5xs/tZ/3odDoURcFgMGAwGMpSLoDx2iMFY5jDoUOHmDx5Mhs2bKBNmzYsXLiQQYMGUa9evVLn9Prrr9O7d2+efvpp3N3/vaN2ZdY3duxYvL298fDwYOPGjRw7dgwnJyc6d+7M/PnzadKkSbm9lsFgQFEUdDqdsS5rPSOsoC5rrM+gN/BI40e4fPkyBr3BKmsE696GIPVVZQaDwie/n2VR1Ekae9jxUF5euY5flp+ZWRug06dP88EHHzBlyhRmzJjBn3/+ycSJE9FqtTz55JNFrpOUlETt2rVNltWuXZv8/HxSUlLw8fEpNiYpKanIMefNm8esWbMKLd+6dWuh093t7e3x9vYmIyODvHvYcOnp6Xe97r365ptvaN26Nd26dSM7O5vVq1fz9ddfGxu/0ggICMDPz49Vq1Yxbty4Qs9XdH0Gg4Eff/yRiIgI3nnnHcaOHUtwcDD5+fnMmTOHvn37snfvXlxcXMrl9fLy8sjOzmbXrl3k5+cDEBUVVS5jWyprrW+M8xioD79t/83cqVQ4a92GBaS+qiVDB1+etOPojZuTT05q2PLzNhzK8U5DWVlZpY41awNkMBho164dc+fOBSA4OJjDhw/zwQcfFNsAQeFTkgv2Oty6vKiY4k5lDgsLY8qUKcbHaWlp+Pn50bdvX5O9GwA5OTlcuHABV1dXHB0djWNn60p33ytFUchIz8DVzbVcTq120qjLNE6jRo04ffo0ANWqVTPW0adPH5O4NWvWMG7cOOLj46lTpw4Azz77LPv372fnzp14eHjw8MMPs2nTJpO9bYqikJ6ejpub213VV5rXBfjtt99Qq9U88MADhXL//PPP8fb2Jj4+nu7du5c5h6Lk5OTg5ORE9+7dUavVREVFERISgkajKZfxLYlOp5P6qjhrr1Hqq3r+PHuNuV8f5HJ6Llp7O2b0b4RHymH69i3fGsvyj7xZGyAfHx+aNWtmsqxp06YmBzTfztvbu9CenOTkZOzt7Y1XZi4u5va9QgW0Wi1abeEbI2o0mkIbRq/Xo1KpsLOzM17pOCsvnxYzzdOpH3m7H85laJ/37NlD586d+b//+z+eeOIJXnvtNS5dulToqs2hoaG88847LFiwgOXLlzNr1iy2bt3K3r17qVbt5pV0O3bsyPz589HpdMafX8H00Pz585k3b16JuWzZsoVu3bqV+XUBNm/ezODBg7G3L/wWLtj75OXlVW5Xo7azs0OlUpncGLWo94c1kfqqPmuvUeqzfHqDwv+2n2TxthMYFGhQ04UVoW24z8uJyMjD5V5jWcYyawPUtWtXjh8/brLsxIkT+Pv7F7tO586d+eGHH0yWbd26lXbt2hkL79y5M1FRUSZ7JrZu3UqXLl3KMfuqydXVlbNnz3L//ffj7e3N1atX8fX1LRSnUqn473//y7Bhw/D19WXp0qX89ttvxr0yAHXq1CE3N5ekpKRC2+w///kPI0aMKDGXW8cqy+vCzePHbj3wvYCiKEyZMoX777+fFi1alPj6wvZk5mXiOs8VgOt9ruOp8TRvQkJYsSvpuby0LpbdJ1MAGBpch9kPt8BFa28RxzeZtQF66aWX6NKlC3PnzmX48OH8+eeffPTRR3z00UfGmLCwMBISEvj8888BeP7551m+fDlTpkzh2WefZc+ePaxatYo1a9YY15k0aRLdu3dnwYIFPPTQQ2zatIlt27axe/fuCqnDSaPmyNv9ShVrMBhIT0vHzd2tXPZOOGnKNnl64MABAIKCggDIzs42TuXdbtCgQTRr1sy4F6Z58+amr/3PPbKKmnOtXr06Xl5eZcqttK979OhRLl68WGjqC2DChAkcOHCgwra1EEKIO/vjZAqT1sVyJT0XR40dsx9qwWPt/MydlgmzNkDt27dn48aNhIWF8fbbb1O/fn2WLFnCqFGjjDGJiYmcP3/e+Lh+/fpERkby0ksvsWLFCnx9fVm2bBmPPvqoMaZLly6sXbuW119/nTfeeIOGDRuybt06OnbsWCF1qFQqnB1K96M0GAzkO6hxdrA3y81CY2Njue+++4wHB3t5eXH9+vUiY3/++WeOHTuGXq8vcvrw2rVrANSsWbPQc/PmzburKbDSvO73339PSEiIsQEr8OKLL/L999+za9cu6tatW+JrCyGEKH96g8LSX+J5/9d4FAUa13ZlRWgbGtV2M3dqhZj9bvCDBg1i0KBBxT4fHh5eaFmPHj2Ijo4ucdxhw4YxbNiwe03P6sTGxtKqVSvj4+DgYL788stCcdHR0Tz22GN8+OGHrF27ljfeeINvvvnGJObQoUPUrVu3yD09dzsFVprX3bRpE88884zxsaIovPjii2zcuJEdO3ZQv379El9XCCFE+buclsOktTHsPX3zn+Ph7eoya0gLnMrzNK9yZPYGSFSu2NhYhgwZYnzcr18/wsLCuH79uvEg47NnzzJw4ECmT5/O6NGjadasGe3bt+fvv/+mbdu2xnV/++23QtdkKnA3U2Cled3k5GT279/Pd999Z1xv/PjxREREsGnTJtzc3IwHwHt4eBTaSySEEKL87TpxhZfWxXI1Mw9nBzX/faQFjwRb9p54s98LTFQeg8HAwYMHTfYABQUF0a5dO77++mvg5rTWgw8+yJAhQ5gxYwYAbdu2ZfDgwbz22mvG9XJycti4cWOJF60si9K+7g8//EDHjh2pVauWcdkHH3xAamoqPXv2xMfHx/i1bt26cslNCCFE0fL1Bt79+RhjVv/J1cw8Ar3d+OHF+y2++QHZA2RT7OzsyMzMLLT8jTfeYOrUqTz77LNUr16do0ePForZtGmTyeNVq1bRsWNHOnXqVC65lfZ1N23aZLIHC/69DpQQQojKk5iazcQ1Mew/e/M40lEd6/HGoGY4lvHkHHORBkgwYMAA4uPjSUhIwM+vdEfpazQa3n///QrOrLD777+fkSNHVvrrCuugtlPzYMMHSb6SjNquanxIC2GJth9LZsrXsVzP0uGqtWfe0CAGtyp8SRVLJg2QAG5eOqAsnnvuuQrKpGTTpk0zy+sK6+Bo78imEZuIjIzE0b7oyz8IIYqn0xtY+PNxPtx1844CLeq4s3xkGwK8yue2Q5VJGiAhhBBC3NHF61m8uCaGmPM3AHiqSwBhAwLR2lfNvanSAAkhhBCiRFsPJ/HKtwdIzdbh5mjPu8Na0r+Fj7nTuifSAAkhbEZmXia1FtZCr9eT1CdJboUhxB3k5RuYt+Uoq38/C0Cruh4sD22DX3Vn8yZWDqQBEkLYlCxd4Vu3CCEKO381iwlrojlwMRWAcffX59X+gTjYW8cVdKQBEkIIIYSJLQcTmfbtAdJz8/Fw0rDwsVaENCt8a6KqTBogIYQQQgCQo9MzN/Ion+85B0Cbep68H9qGOp7Wd1V9aYCEEEIIwZmUTCZERHP4UhoA/+nRgKl9m6BRW8eU1+2ssypxV1Qqlck9tu7G2LFjGTVqVPkkJIQQolJ8H3eJwe/v5vClNKq7OLB6bHvCHmxqtc0PSANkU5566ikefvjhYp9PTEzkwQcfvKfXWLJkCf/73/+Mj3v27MnkyZPvuF5p48pLeHg4KpWq0FdOTk6l5SCEEOaWo9MTtuEgE9fEkJGbT4eA6kRO7EavJrXuvHIVJ1Ngwsjb2/uex/Dw8EClUpVDNhXP3d2d48ePmyxzdJSrA1szO5Ud3et15+rVq9ip5P8/YdtOJmcwISKaY0npqFQwodd9TOrdCHsr3utzK9uoUpTKrVNgZ8+eRaVS8fXXX9OtWzecnJxo3749J06cYP/+/bRr1w5XV1f69+/PlStXjGPcOgX21FNPsXPnTpYuXWrcw3L27FkzVFY0lUqFt7e3yZewbk4aJ7Y9sY3/NvovThrrO6hTiNLaEH2RIct3cywpHS9XBz5/ugMv921iM80PSANUvjIzi/+6fWqlpNjs7NLFVoK33nqL119/nejoaOzt7Rk5ciTTpk1j6dKl/Pbbb5w6dYo333yzyHWXLl1K586defbZZ0lMTCQxMbHUN1u9k7lz5+Lq6lri12+//VbiGBkZGfj7+1O3bl0GDRpETExMueQmhBCWKisvn1e+iWPK13Fk5enp3KAGkRO70a1RTXOnVulkCqw8uboW/9yAAfDjj8aHKm9vyCrmgmw9esCOHf8+DgiAlJTCcYpyV2mWxdSpU+nXrx9w84apI0eO5JdffqFr164AjBs3jvDw8CLX9fDwwMHBAWdn53Lfu/L8888zfPjwEmPq1KlT7HOBgYGEh4cTFBREWloaS5cupWvXrsTFxdGoUaNyzVUIISzBicvpjP8qmvjkDFQqmNS7ES8+0Ai1XdU4bKG8SQMkStSyZUvj97Vr37wIVlBQkMmy5OTkSs+revXqVK9e/a7X79SpE506dTI+7tq1K23atOH9999n2bJl5ZGisECZeZkELAkgLy+Pc33Oya0whE1QFIVv/rrIm98fIkdnoKablqWPt6ZLQy9zp2ZW0gCVp4yM4p9Tm94tV0lKQmVXzAzk7cvNeNyMRqMxfl9wcPPtywwGQ6XnNXfuXObOnVtizJYtW+jWrVupxrOzs6N9+/bEx8eXR3rCgqVkF7E3VQgrlZmbz+vfHWJjTAIA3Rp5sXhEa7xctWbOzPykASpPLi5liy2uAbqXcS2Mg4MDer2+3Me91ymw2ymKQmxsrMneLSGEqMqOJqYx/qtoTqdkYqeCl/s24f96NMTORqe8bicNkI1JTU0lNjbWZFn16tWpV69ehbxeQEAA+/bt4+zZs7i6ulK9enXsimn8rly5Uii34s7OutcpsFmzZtGpUycaNWpEWloay5YtIzY2lhUrVtz1mEIIYQkURSHiz/PM+uEIefkGvN0dWTYymA717/4z0xpJA2RjduzYQXBwsMmyMWPGFHsg872aOnUqY8aMoVmzZmRnZ3PmzBkCAgKKjI2IiCAiIsJk2VtvvcXMmTPLPa8bN27w3HPPkZSUhIeHB8HBwezatYsOHTqU+2sJIURlSc/REbbhIJsPJALQq0lN3hvemuouDmbOzPJIA2RDwsPDS2x0lFvOKgsICDB5DDev1nz7sqeeeoqnnnrK+Hj16tWkpaUZHzdu3Jg9e/bcMbcdt571VgkWL17M4sWLK/U1hRCiIh1KSGVCRDRnr2Zhb6filX5NeLZbA5nyKoY0QEIIIUQVpigKn+85x39/PEqe3kAdTyeWjQymrX81c6dm0aQBEkLYDDuVHW192pJ6I1VuhSGsQmq2junrD7DlUBIAfZrWZuFjLfF0limvO5EGSAhhM5w0TuwZu4fIyEi5FYao8mIv3GBCRDQXr2ejUauY/mBTnu4aUGXux2hu0gAJIYQQVYiiKKzafYYFPx1Dp1fwq+7E8pFtaOXnae7UqhRpgIQQQogq4kZWHlO/OcC2o5cBeLCFN/MfbYmHk+YOa4rbSQMkhLAZWbosmq1oRlZWFvEh8XhoPMydkhCl9ve567wYEc2l1Bwc1Ha8Pqgpozv5y5TXXZIGSAhhMxRF4VzqOeP3QlQFBoPCR7+d5t2fj6M3KATUcGZ5aBta1JEG/l6Y9TSImTNnolKpTL5Kumv4U089VShepVLRvHlzY0x4eHiRMTk5OZVRkhBCCFFurmXm8fRn+5m/5Rh6g8LgVr788OL90vyUA7PvAWrevDnbtm0zPlbfdtPQWy1dupT58+cbH+fn59OqVSsee+wxkzh3d3eOHz9usszR0bGcMhZCCCEq3v6z15nyzUGS0nLQ2tvx1uDmjOzgJ1Ne5cTsDZC9vX2Je31u5eHhgYfHv13vd999x/Xr1xk7dqxJ3J32JAkhhBCWymBQ2HpRxZa9+zEo0KCmCytC29DUx93cqVkVszdA8fHx+Pr6otVq6dixI3PnzqVBgwalWnfVqlX06dMHf39/k+UZGRn4+/uj1+tp3bo1s2fPLnT/q1vl5uaSm5trfFxwKwedTodOpzOJ1el0KIqCwWDAYDCUtkyjguMOCsawNrfXN3fuXCIjI4mNjcXBwYFr164VWuf8+fNMmDCB7du34+TkxMiRI3n33XdxcLCcC3kZDAYURUGn0xm32+3vDWtRUJc11ndrTUX9flsLa96GYN31pWTk8vI3B/jjws3ZkIdb+TBzcFNctPZWVW9FbcOyjKdSzHgk4JYtW8jKyqJx48ZcvnyZOXPmcOzYMQ4fPkyNGjVKXDcxMRE/Pz8iIiIYPny4cfnevXs5efIkQUFBpKWlsXTpUiIjI4mLi6NRo0ZFjjVz5kxmzZpVaHlERATOzs4mywr2WPn5+VnUH2hLNW/ePDw8PLh06RJffPEF586dM3ler9fTrVs3vLy8mDNnDteuXeOFF15g0KBBvPPOO2bKurC8vDwuXLhAUlIS+fn55k5H3KUcfQ6PH3wcgLVBa3FUy9S4sBzxqSo+j7cjTadCY6cwrL6BjjUVZMar9LKysggNDSU1NRV395L3mJm1AbpdZmYmDRs2ZNq0aUyZMqXE2Hnz5vHee+9x6dKlEhsRg8FAmzZt6N69O8uWLSsypqg9QH5+fqSkpBT6Aebk5HDhwgUCAgLu6rgiRVFIT0/Hzc2tUudxr1y5QqtWrXjxxRcJCwsDYN++ffTo0YPvv/+evn37lmm8pKQknJycTKYkofj6wsPDmTJlSqE9QFu2bGHIkCGcO3cOX19fANauXcvTTz9NUlLSHd/AlSUnJ4ezZ8/i5+eHWq0mKiqKkJAQNBrru/aGTqez2vqydFl0/rQzGZkZRD8fjYezdR5Ias3bEKyvPr1B4X87TrN8xykMCjSs6cxjvmk8+ZB11FeUitqGaWlpeHl5laoBMvsU2K1cXFwICgoiPj6+xDhFUfj0008ZPXr0HffC2NnZ0b59+xLH1Gq1aLXaQss1Gk2hDaPX61GpVNjZ2WFnZ3oSXWZeZrGvobZT42jvaJw+ydJlFVrfmLPKzuQy/cWN6+LgUuzr3a527dp8+umnPPzww/Tr14/AwECefPJJXnjhBfr371/qcQrMnDmTuLg4tm7datIEFdRX8DMqUPD97TXv27ePFi1aULduXeOyBx98kNzcXGJiYujVq1eZc6sIdnZ2qFQqNBqN8UD9ot4f1sQa6/PQeBD3nzgiIyPxcPawuvpuZ43b8FbWUF9yWg6T1say5/RVAIa3q8vrDzZh+7afraK+OynvGssylkU1QLm5uRw9epRu3bqVGLdz505OnjzJuHHj7jimoijExsYSFBRUXmkWy3Wea7HPDWg0gB9DfzQ+9l7kTZYuq8jYHv492PHUDuPjgKUBpGSlFIpT3irbzrsBAwbw7LPPMmrUKNq3b4+jo6PJWXVlsXTpUoYMGUJISAhbt27F09PzrsZJSkqidu3aJsuqVauGg4MDSUlJdzWmEEJUBb/FX+GldbGkZOTh7KBmzsMtGNqmrlUd62PJzHodoKlTp7Jz507OnDnDvn37GDZsGGlpaYwZMwaAsLAwnnzyyULrrVq1io4dO9KiRYtCz82aNYuff/6Z06dPExsby7hx44iNjeX555+v8HqqgoULF5Kfn8/XX3/NV199VeI03tSpU4u8ppJKpcLZ2Zlt27axf/9+XnvttXvKqaipQEVR5FRPIYRVytcbWPjzcZ789E9SMvII9Hbj+wn3M7RN3TuvLMqNWfcAXbx4kZEjR5KSkkLNmjXp1KkTe/fuNZ7VlZiYyPnz503WSU1NZf369SxdurTIMW/cuMFzzz1HUlISHh4eBAcHs2vXLjp06FDh9WSEZRT7nNrO9PpGSVOSSpwCu9XZSWfvObcCp0+f5tKlSxgMBs6dO0fLli2LjX311Vd55plninxOURQmTpzIiRMnmDp16l3n4+3tzb59+0yWXb9+HZ1OV2jPkBD3KkuXRbuP2pGRkUHPkJ5yKwxR6RJTs5m0JpY/z948HjK0Yz3eHNQMR03x18ATFcOsDdDatWtLfD48PLzQMg8PD7Kyip46Ali8eDGLFy++19TuSlmOyXFxcCm2AbqXcUuSl5fHqFGjGDFiBIGBgYwbN46DBw8W22jUrFmTmjVrFvncyy+/THx8PDt27KB+/fp3nVPnzp3573//S2JiIj4+PgBs3boVrVZL27Zt73pcIYqiKApHU44avxeiMm0/lsyUr2O5nqXDVWvP3KFBDGnla+60bJZFHQMkKtZrr71Gamoqy5Ytw9XVlS1btjBu3Dg2b95c5rHGjh3Liy++SEBAQIlx58+f59q1a5w/fx69Xk9sbCwA9913H66urvTt25dmzZoxevRo3n33Xa5du8bUqVN59tlnLeYMMCGEuBe6f6a8Ptx1GoDmvu6sCG1DgFf5/HMr7o40QDZix44dLFmyhO3btxsbiy+++IKWLVvywQcf8H//939lGq+o46+K8uabb/LZZ58ZHxdckHL79u307NkTtVrNjz/+yAsvvEDXrl1xcnIiNDSUhQsXlikfIYSwRAk3snkxIpro8zcAGNPZn7ABTWXKywJIA2QjevbsWejMgnr16nHjxo0Kfd3w8PAipzJvz+Nu9kIJIYQlizpymanfxJGarcPN0Z53Hm3Jg0E+5k5L/EMaICGEEKIc5eUbWPDTMVbtPgNAq7oevD+yDfVqON9hTVGZpAESQgghysmFa1lMiIgm7mIqAE93rc/0BwNxsDfrVWdEEaQBEkLYDJVKhb+HP1lZWXKdKVHufjqUyCvfHiA9Jx8PJw0LH2tFSDO5nIelkgZICGEznDXOxI+PJzIyEmeNTEeI8pGj0zMv8iif7bl5s+c29TxZNjKYutXkPWbJpAG6S3INEdsi21sIUZSzKZmMj4jm8KU0AP7TowFT+zZBo5YpL0snDVAZFdxoLSsrCycnpztEC2tRcPFNjUZjvOGrEMK2/RB3ibANB8nIzaeas4ZFw1vTK7CWudMSpSQNUBmp1Wo8PT1JTk4GwNnZuUzHEhgMBvLy8sjJySn1laCrEmurT1EUsrKySE5OxtPTE7VaLQ1QFZaty6bb6m6k3kilV0gvq7/TtqgYOTo9b28+QsS+m7dqah9QjWUjg/HxkH+KqxJpgO6Ct7c3gLEJKgtFUcjOzsbJyckqD8K01vo8PT2N211UXQbFwN+Jfxu/F6KsTl3JYPxX0RxLSkelgvE972Nyn0bYy5RXlSMN0F1QqVT4+PhQq1atQhcXvBOdTseuXbvo3r27Vf73aY31aTQa1Gq5aqsQtm5jzEVe23iIrDw9NVwcWPJ4a7o1Kvp+icLySQN0D9RqdZn/MKrVavLz83F0dLSaBuFW1l6fEML2ZOfpeev7Q3z910UAOjeowdLHW1PL3dHMmYl7IQ2QEEIIUYz4y+m88FU08ckZqFQw8YFGTOzdCLWd9Uzx2yppgIQQQojbKIrCN39f5M1Nh8jRGajppmXpiNZ0uc/L3KmJciINkBBCCHGLzNx83vjuEBtiEgDo1siLRcNbU9NNa+bMRHmSBkgIYVO8nLzIy8szdxrCQh1NTGNCRDSnrmRip4KX+zbh/3o0xE6mvKyONEBCCJvh4uDCpZcuERkZiYuDi7nTERZEURTW/HmBWT8cJjffgLe7I8tGBtOhfnVzpyYqiDRAQgghbFp6jo4ZGw/xQ9wlAHo2qcmi4a2p7uJg5sxERZIGSAghhM06lJDKhIhozl7NQm2nYlq/JjzbrYFMedkAaYCEEDYjW5dN/y/7c/XqVXrp5FYYtkxRFL7Ye445m4+Spzfg6+HI+6FtaOtfzdypiUoiDZAQwmYYFAO7zu8yfi9sU2q2jrANB4g8mARAn6a1WfhYSzydZcrLlkgDJIQQwmbEXbjBhDXRXLiWjUat4tX+gYy7v75V3btQlI40QEIIIayeoih8+vtZ5m85ik6vULeaE8tD29Daz9PcqQkzkQZICCGEVbuRlccr3x4g6shlAPo392bBsJZ4OMkxYLZMGiAhhBBWK/r8dV6MiCHhRjYOajteH9SU0Z38ZcpLSAMkhBDC+hgMCh//dpp3fz5OvkHBv4YzK0Lb0KKOh7lTExZCGiAhhE1x1jij1+vNnYaoQNcy85j6TRy/HksGYFBLH+YNDcLNUaa8xL+kARJC2AwXBxduvHJDboVhxf48c42Ja2JISsvBwd6OmYObM7KDn0x5iUKkARJCCFHlGQwKH+w8xaKoE+gNCg28XFgxqg1NfdzNnZqwUNIACSGEqNJSMnJ5aV0sv8WnAPBIcB3mPNwCF638iRPFszPni8+cOROVSmXy5e3tXWz8jh07CsWrVCqOHTtmErd+/XqaNWuGVqulWbNmbNy4saJLEUJUATn5OTy07iFmn55NTn6OudMR5WDPqasMWPobv8Wn4Kix451HW7JoeCtpfsQdmf0d0rx5c7Zt22Z8rFar77jO8ePHcXf/d7dmzZo1jd/v2bOHESNGMHv2bB555BE2btzI8OHD2b17Nx07dizf5IUQVYreoGfLqS3G70XVZVDg/V9PsXzHKQwKNKrlyopRbWhc283cqYkqwuwNkL29fYl7fYpSq1YtPD09i3xuyZIlhISEEBYWBkBYWBg7d+5kyZIlrFmz5l7TFUIIYWZX0nP53xE74tNOAfBY27rMeqg5zg5m/5MmqhCzv1vi4+Px9fVFq9XSsWNH5s6dS4MGDUpcJzg4mJycHJo1a8brr79Or169jM/t2bOHl156ySS+X79+LFmypNjxcnNzyc3NNT5OS0sDQKfTodPp7qKq4hWMV97jWgprrw+sv0Zrru/Wmiri99tSWPM2/P3UVV7+5gBXM+1w0qh5e0hTHm7tCyhWU681b78CFVVjWcZTKYqilOurl8GWLVvIysqicePGXL58mTlz5nDs2DEOHz5MjRo1CsUfP36cXbt20bZtW3Jzc/niiy9YuXIlO3bsoHv37gA4ODgQHh5OaGiocb2IiAjGjh1r0uTcaubMmcyaNavQ8oiICJydncupWiGEueXoc3j84OMArA1ai6Pa0cwZidLSK/DTBTuiElQoqPBxVhjbWE9tJ3NnJixJVlYWoaGhpKammhwqUxSzNkC3y8zMpGHDhkybNo0pU6aUap3BgwejUqn4/vvvgZsN0GeffcbIkSONMV999RXjxo0jJ6fogx6L2gPk5+dHSkrKHX+AZaXT6YiKiiIkJASNxvouymXt9YH112jN9WXmZVJtYTUAkicl4+niad6EKoi1bcOktBymfHOQ/WevA/BYG1862J9nYH/rqO921rb9ilJRNaalpeHl5VWqBsjsU2C3cnFxISgoiPj4+FKv06lTJ7788kvjY29vb5KSkkxikpOTqV27drFjaLVatFptoeUajabC3nwVObYlsPb6wPprtMb6NMq/9Vhjfbezhhq3H0/m5a/juJaZh4uDmnmPtuTBZjWJjDxvFfWVxNrrg/KvsSxjmfU0+Nvl5uZy9OhRfHx8Sr1OTEyMSXznzp2Jiooyidm6dStdunQptzyFEEJULJ3ewLwtRxm7ej/XMvNo7uvO5ondGNLK19ypCSth1j1AU6dOZfDgwdSrV4/k5GTmzJlDWloaY8aMAW6ewZWQkMDnn38O3DzDKyAggObNm5OXl8eXX37J+vXrWb9+vXHMSZMm0b17dxYsWMBDDz3Epk2b2LZtG7t37zZLjUIIy+Hi4ELejDy5FYaFS7iRzcQ1Mfx97uaU15Od/ZkxoCmOmjtfJkWI0jJrA3Tx4kVGjhxJSkoKNWvWpFOnTuzduxd/f38AEhMTOX/+vDE+Ly+PqVOnkpCQgJOTE82bN+fHH39kwIABxpguXbqwdu1aXn/9dd544w0aNmzIunXr5BpAQghRBWw7cpmXv4kjNVuHm9aeBcNaMiCo9LMCQpSWWRugtWvXlvh8eHi4yeNp06Yxbdq0O447bNgwhg0bdi+pCSGEqER5+Qbe+ekYn+w+A0DLuh4sH9mGejXkTFxRMSzqIGghhKhIOfk5jNowiqTEJB7If8DqDzCtKi5cy2LCmhjiLtwA4Omu9Zn+YCAO9hZ1mKqwMtIACSFsht6gZ8OxDcbvhfn9dCiRV749QHpOPu6O9ix8rBV9m5ft7gBC3A1pgIQQQlS63Hw9c388ymd7zgEQXM+T90cGU7eaTHmJyiENkBBCiEp1NiWTCWuiOZRw87ZD/+negKn9mqBRy5SXqDzSAAkhhKg0mw9cYvr6g2Tk5lPNWcN7w1vxQGDxF6oVoqJIAySEEKLC5ej0zN58hK/23by0SfuAaiwbGYyPh9zMS5iHNEBCCCEq1KkrGYz/KppjSemoVPBCz4a81Kcx9jLlJcxIGiAhhBAV5ruYBGZsPEhWnp4aLg4sHtGa7o1rmjstIaQBEkLYDmeNM9enXufnn3/GWSNnG1Wk7Dw9M78/zLq/LgDQqUF1lj4eTG13RzNnJsRN0gAJIWyGSqXCxcEFR7UjKpXK3OlYrfjL6YyPiObE5QxUKpj4QCMm9m6E2k5+5sJySAMkhBCi3Hzz1wXe3HSYbJ2emm5alo5oTZf7vMydlhCFSAMkhLAZufm5PPvDs1y8eJHe+b3lVhjlKDM3nzc2HWJDdAIA99/nxeIRranppjVzZkIUTRogIYTNyDfk88XBL4zfi/JxLCmN8V9Fc+pKJnYqmBLSmBd63oedTHkJCyYNkBBCiLuiKApr919g5veHyc03UNtdy7LHg+nYoIa5UxPijqQBEkIIUWYZufnM2HCQ7+MuAdCjcU0WDW9FDVeZ8hJVgzRAQgghyuRQQioTIqI5ezULtZ2KV/o14bluDWTKS1Qp0gAJIYQoFUVR+HLvOWb/eJS8fAO+Ho68HxpMW//q5k5NiDKTBkgIIcQdpeXomL7+AJEHkwDo07QW7w5rRTUXBzNnJsTdkQZICCFEiQ5cvMH4iGguXMtGo1bxav9Axt1fXy4mKao0aYCEEDbDWeNMwqQEtv2yTW6FUQqKorD697PM23IUnV6hbjUnloe2obWfp7lTE+KeSQMkhLAZKpWKmi418bD3kL0Xd5CapeOVb+PYeuQyAP2be7NgWEs8nOTikcI6SAMkhBDCRPT567wYEUPCjWwc1Ha8NrApT3b2l6ZRWBVpgIQQNiM3P5fJP03m3MVzciuMIhgMCp/sPs07Px0n36DgX8OZ5SPbEFTXw9ypCVHupAESQtiMfEM+K6NXGr8X/7qemcfL38Tx67FkAAa29GH+0CDcHKVJFNZJGiAhhLBx+89eY+KaGBJTc3Cwt+Otwc0I7VBPpryEVZMGSAghbJTBoPDBzlMsijqB3qDQwMuF5aFtaObrbu7UhKhw0gAJIYQNSsnIZcrXcew6cQWAh1v7MueRIFy18mdB2AZ5pwshhI3Ze/oqE9fEkJyei6PGjreHtOCxdnVlykvYFGmAhBDCRugNCst/PcnSX05gUOC+Wq6sCG1DE283c6cmRKWTBkgIIWxAcnoOk9fG8sepqwA81rYusx5qjrOD/BkQtkne+UIIm+GkceLECyfYvn07Thonc6dTaXbHpzB5XSwpGbk4adT895EWDG1T19xpCWFWduZ88ZkzZ6JSqUy+vL29i43fsGEDISEh1KxZE3d3dzp37szPP/9sEhMeHl5oTJVKRU5OTkWXI4SwcHYqOwI8A6itrY2dyqwff5UiX2/gva3HGf3pPlIycgn0duOHF++X5kcILGAPUPPmzdm2bZvxsVqtLjZ2165dhISEMHfuXDw9PVm9ejWDBw9m3759BAcHG+Pc3d05fvy4ybqOjo7ln7wQQlioG7nwZPjf7D97HYCRHfx4a3BzHDXFf8YKYUvM3gDZ29uXuNfnVkuWLDF5PHfuXDZt2sQPP/xg0gDdaU+SEMI25enzCPsljNMJp+mj72O1t8LYFZ/COwfUZOZfx8VBzdyhQTzUuo650xLCopi9AYqPj8fX1xetVkvHjh2ZO3cuDRo0KNW6BoOB9PR0qlevbrI8IyMDf39/9Ho9rVu3Zvbs2SYN0u1yc3PJzc01Pk5LSwNAp9Oh0+nuoqriFYxX3uNaCmuvD6y/RmuuLysvi0X7Ft38PicLB7WDmTMqXzq9gaW/nOLD384AKgK9XXn/8VYE1HCxqu1pze9RsP76oOJqLMt4KkVRlHJ99TLYsmULWVlZNG7cmMuXLzNnzhyOHTvG4cOHqVGjxh3Xf/fdd5k/fz5Hjx6lVq1aAOzdu5eTJ08SFBREWloaS5cuJTIykri4OBo1alTkODNnzmTWrFmFlkdERODs7HxvRQohLEaOPofHDz4OwNqgtTiqrWdq/HoufBav5kz6zWv53F/bwMMBBjTWf6iTEEZZWVmEhoaSmpqKu3vJVzQ3awN0u8zMTBo2bMi0adOYMmVKibFr1qzhmWeeYdOmTfTp06fYOIPBQJs2bejevTvLli0rMqaoPUB+fn6kpKTc8QdYVjqdjqioKEJCQqxy97u11wfWX6M115eZl0m1hdUASJ6UjKeLp3kTKie/Hr/Cq+sPcSNbh6vWntmDm2CXEGeV2xCs+z0K1l8fVFyNaWlpeHl5laoBMvsU2K1cXFwICgoiPj6+xLh169Yxbtw4vvnmmxKbHwA7Ozvat29f4pharRatVltouUajqbA3X0WObQmsvT6w/hqtsT6N8m891lBfXr6Bd346xie7zwDQsq4Hy0e2wcddQ2RCnFXUWBKpr+or7xrLMpZF7RzNzc3l6NGj+Pj4FBuzZs0annrqKSIiIhg4cOAdx1QUhdjY2BLHFEKIqubCtSwe+3CPsfl5umt9vnm+M/VqyLS9EKVh1j1AU6dOZfDgwdSrV4/k5GTmzJlDWloaY8aMASAsLIyEhAQ+//xz4Gbz8+STT7J06VI6depEUlISAE5OTnh4eAAwa9YsOnXqRKNGjUhLS2PZsmXExsayYsUK8xQphBDl7KdDSUz7No60nHzcHe1Z+Fgr+jaXM1+FKAuzNkAXL15k5MiRpKSkULNmTTp16sTevXvx9/cHIDExkfPnzxvjP/zwQ/Lz8xk/fjzjx483Lh8zZgzh4eEA3Lhxg+eee46kpCQ8PDwIDg5m165ddOjQoVJrE0KI8pabr2de5DHC/zgLQHA9T94fGUzdarLXR4iyMmsDtHbt2hKfL2hqCuzYseOOYy5evJjFixffQ1ZCCGvlpHEi5tkYftv1W5W7Fca5q5lMiIjhYEIqAM91b8Ar/ZqgUVvUkQxCVBkWdRC0EEJUJDuVHc1rNuec07kqdSuMHw8kMn39AdJz86nmrOG94a14ILC2udMSokqTBkgIISxUjk7PnB+P8OXem4cCtPOvxvuhwfh4VK29V0JYImmAhBA2I0+fx+xds4lPjLf4W2GcvpLB+IgYjibevDL9Cz0bMiWkMfYy5SVEuZAGSAhhM3R6HXN2zwFgpX6lmbMp3qbYBGZsOEhmnp4aLg4sGtGaHo1rmjstIayKNEBCCGEhsvP0zPrhMGv3XwCgU4PqLH08mNru1nPLDiEshTRAQghhAU4mpzP+qxiOX05HpYIXH2jEpN6NUNupzJ2aEFZJGiAhhDCzb/++yBvfHSJbp8fLVcuyx1vT5T4vc6clhFWTBkgIIcwkKy+f1787xIboBADuv8+LxSNaU9Ot8L0JhRDlSxogIYQwg2NJaYz/KppTVzKxU8FLfRrzQq/7ZMpLiEoiDZAQQlQiRVFYt/8Cb31/mNx8A7XdtSx9PJhODWqYOzUhbIo0QEIIm+Fo78gfT/3B73/8jqN95Z9ZlZGbz2sbD7Ip9hIAPRrXZNHwVtRwlSkvISqbNEBCCJuhtlPTzrcdyc7JqO3Ulfrahy+lMiEihjMpmajtVEzt24T/dG+AnUx5CWEW0gAJIUQFUhSFL/edZ/bmI+TlG/DxcOT9kcG0C6hu7tSEsGnSAAkhbEaePo9FexdxLPlYpdwKIy1HR9j6g/x4MBGA3oG1WPhYK6q5OFTo6woh7kwaICGEzdDpdYT9GgbAEv2SCn2tAxdvMCEihvPXsrC3UzH9wUDG3V8flUqmvISwBNIACSFEOVIUhfA/zjI38ig6vUIdTyeWhwYTXK+auVMTQtxCGiAhhCgnqVk6pq2P4+fDlwHo17w27zzaCg9ny73rvBC2ShogIYQoBzHnrzMhIoaEG9k4qO2YMSCQMV0CZMpLCAslDZAQQtwDRVH45LczLPjpGPkGhXrVnVkR2oaguh7mTk0IUQJpgIQQ4i5dz8xj6jdx/HIsGYCBLX2YNzQId0eZ8hLC0kkDJIQQd+Gvs9d4cU0Miak5ONjb8eagZozqWE+mvISoIqQBEkLYDEd7R6JGRbF37967vhWGwaCwctcp3tt6Ar1Bob6XC8tDg2nuK1NeQlQl0gAJIWyG2k5ND/8eZB7OvKtbYVzNyGXK13HsPHEFgIda+/LfR4Jw1cpHqRBVjfzWCiFEKew9fZVJa2O4nJaLo8aOWUOaM7ydn0x5CVFFSQMkhLAZOr2OD/76gMNXDhOiDynVrTD0BoUV20+yZNsJDArcV8uVFaFtaOLtVgkZCyEqijRAQgibkafPY9LWSQAs0C/AGecS45PTc3hpXSy/n7wKwLC2dXn7oeY4O8hHpxBVXZl/i48fP86aNWv47bffOHv2LFlZWdSsWZPg4GD69evHo48+ilarrYhchRCi0vx+MoVJa2NJycjFSaNmzsMteLRtXXOnJYQoJ3alDYyJiSEkJIRWrVqxa9cu2rdvz+TJk5k9ezZPPPEEiqLw2muv4evry4IFC8jNza3IvIUQokLoDQqLok7wxKp9pGTk0qS2Gz+82FWaHyGsTKn3AD388MO88sorrFu3jurVqxcbt2fPHhYvXsx7773HjBkzyiVJIYSoDJfTcpi4JoZ9Z64BMLKDH28Nbo6jpuxnjAkhLFupG6D4+HgcHBzuGNe5c2c6d+5MXl7ePSUmhBCVaeeJK7y0LpZrmXm4OKiZOzSIh1rXMXdaQogKUuoGqDTND0BWVhbOzs6ljhdCCHPK1xt4L+oEH+w4BUBTH3dWhAbToKarmTMTQlSkUh8DdKuePXty8eLFQsv37dtH69atSz3OzJkzUalUJl/e3t4lrrNz507atm2Lo6MjDRo0YOXKlYVi1q9fT7NmzdBqtTRr1oyNGzeWOichhO24dCObxz/aa2x+RnfyZ+MLXaT5EcIG3FUD5O7uTsuWLVm7di0ABoOBmTNn0r17d4YMGVKmsZo3b05iYqLx6+DBg8XGnjlzhgEDBtCtWzdiYmKYMWMGEydOZP369caYPXv2MGLECEaPHk1cXByjR49m+PDh7Nu3725KFUJYEa29lu+Gf8fr9V9nz6k0Biz7jb/OXcdNa8+K0DbMfriFHO8jhI24q4tZfP/996xcuZJnnnmG77//nrNnz3L+/Hl+/PFH+vTpU7YE7O3vuNenwMqVK6lXrx5LliwBoGnTpvz1118sXLiQRx99FIAlS5YQEhJCWFgYAGFhYezcuZMlS5awZs2aMuVGZiaoi/gwVKvB0dE0rjh2duDkZBKrzsm5uc7tF2G7PTYrCxSl6HFVKnB2vrvY7GwwGIrP2cXl7mJzciAnp/j6bo/V64sf19n5Zt4AubmQn18+sU5ON3/OAHl5oNOVPVanK1yjo+O/75U7jXtrrE53M744Wi3Y25c9Nj//5s+iOA4O/+Z+e+zt9d0aq9ff3HbFKYgva6zBcPO9Vh6x9vY3fxZw83ciK+vfp4CQWt2ITMpjSvh+9HZqgvy9WB4ajH9155J/l8vye3+PnxGlji3u916nQ3379reUz4iSfu9LG6vTmdZiaZ8RRSnLZ8Stf3cs8TOipNiyfkYU9beiqNiyfEaUlnIPpk+frqhUKkWj0Si///57mdd/6623FGdnZ8XHx0cJCAhQRowYoZw6darY+G7duikTJ040WbZhwwbF3t5eycvLUxRFUfz8/JRFixaZxCxatEipV69esePm5OQoqampxq8LFy4ogJJ681es0Jf+wQeVvLw845fB2bnIOAUUfffuprFeXsXHtm1rGuvvX2ysoWlT09imTYuP9fc3idW3bVt8rJeXaWz37sXHOjubxj74YLGxCpjGDh1acuz16//Gjh5dcmxCgjE2//nnS449ceLf2ClTSo6Nifk39vXXS4zV/fHHv7Hz5pUcGxX1b+zSpSXHfvedMVb3ySclx0ZE/BsbEVFy7Cef/Bv73XclxuYvXfpvbFRUybHz5v0b+8cfJce+/vq/74mYmJJjp0z5N/bEiZJjn3/+39iEhBJjo3sNUdKzcm7GXr9eYqx+6FCT93CJsRbwGZHq56dkZmZa7WfED2vXGuuzts+I7C1blO+++07JzMy02s+IzMxMZce775YcexefESkpKQqgpKam3rEHuas9QNevX+eZZ57hl19+4cMPP2Tnzp307duXd955hxdeeKHU43Ts2JHPP/+cxo0bc/nyZebMmUOXLl04fPgwNWrUKBSflJRE7dq1TZbVrl2b/Px8UlJS8PHxKTYmKSmp2DzmzZvHrFmzSp13cnIy+yIjjY8H6vXF7kq7dvUqv98S2z8vj+IuE5mamsquW2JDsrKKvU5tekYG22+J7ZWRgXsxsdlZWUTdEts9NZVqxcTm5eXx0y2xXa9exauYWL1eT+QtsR2TkylpX96tse2Skijp/Jqff/4Z/T//QQdfvEi9EmK3bdtGnocHAC3PnaN+CbHbt28n+5/3R7PTp2lUQuxvv/1G+rlzADSJjyewhNjff/+dG8nJANx37BjNS4jdu3cvV//5L7/+4cO0LCH2r7/+4vI/3/vFxdGmhNiYmBgu/fNfvG9MDO1LiD0QF8eFf7ZH7b/+olMJsYcPH+bMP7E1Dh7k/hJijx07xsl/Yj3j4+lRQmx8fDzH/4l1O3+eB0qIPX36NEf+iXW6fJm+JcSeP3eOA//EOqSm8uAtz+ns4Kt/fuCjDkAN0vll608AqHNyGFTCuIlJSfx1y3v4oRJiLeEzAiAqKsr4vbV9RsC/9VnbZ8Rff/0FQUFERUVZ92dECXFwd58RWbfs8b0TlaIoSqmj/1GnTh3q16/PF198Qf36N99K69at44UXXqBTp078+OOPZR0SgMzMTBo2bMi0adOYMmVKoecbN27M2LFjjdNbcPNNdf/995OYmIi3tzcODg589tlnjBw50hjz1VdfMW7cOHKK2S2Xm5trcuHGtLQ0/Pz8SDl3Dnf3Ij4y7mH3tu7GDX799VceeOCBwvchsoIpMF1OTvH1WckUmE6nK1yjFU2BFaqvik+B5aZlsOSXeL7adxEDOZzweAKA5GfP4OnuVex0WSFVaApMp9Px6/btPDBo0L/vUQv5jCiPKTCdTkfU778T0rfvzfos7DOiSGX4jNCp1UT9+ishISFoCuKLU0WnwHQ6HVE//URIt27F35PvLj4j0tLS8PLyIjU1tei/37e4qz1Azz//PK+99hp2dv8eQz1ixAi6du3K2LFj72ZIAFxcXAgKCiI+Pr7I5729vQvtyUlOTsbe3t64x6i4mNv3Ct1Kq9UWefsOjacnmjv8AAHw9LxzzC2xekfHm2Pf6UaM//zHUipliS3FDSDvOtbRsXT1VWQOFR2r05VcY1nHdS7pf/h7iL31D2VZYkuq759tXOpxSxsL/zYi5Rh7/moW49cc4WBCKjg4MqaLP2/H/JOehycal9vO9irLMQRl/L2vkNjifu91OvRaLRqN5t9taCmfEeURq9OBSvVvfZaeb1lj/2mOjPVZ2mfEnWJL+3uvVpfub2GBUvzel3os7vIssDfeeMOk+SlQt25dk12uZZWbm8vRo0fx8fEp8vnOnTsXGn/r1q20a9fOWHRxMV26dLnrvIQQVU/kwUQGLvuNgwmpeDprWDWmHdP6NzV3WkIIC1HqBuj8+fNlGjghIeGOMVOnTmXnzp2cOXOGffv2MWzYMNLS0hgzZgxw8wyuJ5980hj//PPPc+7cOaZMmcLRo0f59NNPWbVqFVOnTjXGTJo0ia1bt7JgwQKOHTvGggUL2LZtG5MnTy5T/kKIqilHp+f17w7ywlfRpOfm086/GpETu9G7afF7gYUQtqfUDVD79u159tln+fPPP4uNSU1N5eOPP6ZFixZs2LDhjmNevHiRkSNH0qRJE4YOHYqDgwN79+7F398fgMTERJPGq379+kRGRrJjxw5at27N7NmzWbZsmfEUeIAuXbqwdu1aVq9eTcuWLQkPD2fdunV07NixtKUKIaqoMymZDP3fH3y59+bnxgs9G7LmuU74epZy970QwmaU+higo0ePMnfuXPr3749Go6Fdu3b4+vri6OjI9evXOXLkCIcPH6Zdu3a8++67PPjgg3ccs+BCisUJDw8vtKxHjx5ER0eXuN6wYcMYNmzYHV9fCGE9NsUmMGPDQTLz9NRwcWDRiNb0aFzT3GkJISxUqRugixcvsmDBAubMmcOWLVvYtWsXZ8+eJTs7Gy8vL0aNGkW/fv1o0aJFReYrhBAmcnR6Zn5/mLX7LwDQsX51lo0MprZ7GQ7AFkLYnFI3QMHBwSQlJVGzZk1efvll9u/fX+S1eoQQorKcTE5n/FcxHL+cjkoFLz7QiIkP3Ie9uujZfa29lohHIoiJiUFrX4azzoQQVqfUDZCnpyenT5+mZs2anD17FkNJ130QQogKtv7vi7z+3SGydXq8XLUsfbw1Xe8r7pJ8N9nb2TOs6TCczzhjb3dXVwERQliJUn8CPProo/To0QMfHx9UKhXt2rVDXdR9srh5RUYhhKgIWXn5vLnpMN/+fRGArvfVYPGI1tRykykvIUTplboB+uijjxg6dCgnT55k4sSJPPvss7i5uVVkbkIIYeJ4UjrjI6I5mZyBnQom92nM+F73obZTlWr9fEM+3x79lpgbMfQ19EVDGS5eJ4SwKmXaB9y/f38A/v77byZNmiQNkBCiUiiKwtd/XeCt7w+TozNQ213L0seD6dSgbMch5ubnEroxFIAZ+TNw0srp8ULYqruaBF+9enV55yGEEEXKyM3n9Y0H+S72EgDdG9dk8fBW1HCVg5iFEHdPjgIUQlisI5fSmBARzemUTNR2Kl7u25jnuzfErpRTXkIIURxpgIQQFkdRFL7ad563Nx8hL9+Aj4cj748Mpl1AdXOnJoSwEtIACSEsSlqOjrANB/nxQCIAvQNrsfCxVlRzKcOd2oUQ4g6kARJCWIyDF1OZsCaac1ezsLdTMf3BQMbdXx+VSqa8hBDlSxogIYTZKYrCZ3+cZW7kMfL0Bup4OrE8NJjgetXMnZoQwkpJAySEMKvULB3T1sfx8+HLAPRtVpt3h7XCw7n8r9HjoHbgk0GfEBcXh4NaptSEsGXSAAkhzCb2wg0mRERz8Xo2GrWKGQOa8lSXgAqb8tKoNTzZ8kkiL0aiUctFEIWwZdIACSEqnaIorNp9hvlbjpFvUKhX3ZnlocG0rOtp7tSEEDZCGiAhRKW6kZXH1G/i2HY0GYCBQT7MezQId8eK3yOTb8gn8mQkf6X+JbfCEMLGSQMkhKg0f5+7xosRMVxKzcHB3o43BjXjiY71Ku0sr9z8XB7++mEAXs5/WW6FIYQNkwZICFHhDAaFD3edZuHW4+gNCvW9XFgeGkxzXw9zpyaEsFHSAAkhKtTVjFymfB3HzhNXAHiotS//fSQIV618/AghzEc+gYQQFWbf6atMXBvD5bRctPZ2vP1Qc4a385MLGwohzE4aICFEudMbFP63/SSLt53AoEDDmi78b1Rbmni7mTs1IYQApAESQpSzK+m5vLQult0nUwB4tE1dZj/cHGcH+bgRQlgO+UQSQpSbP06mMHFtLCkZuThp1Mx+uAXD2tY1d1pCCFGINEBCiHumNygs/SWe93+NR1GgSW03locG06i2ZU15OagdWNp3KYcPH5ZbYQhh46QBEkLck8tpOUxaG8Pe09cAeLy9H28Nbo6Tg9rMmRWmUWv4v3b/R2Sy3ApDCFsnDZAQ4q7tOnGFl9bFcjUzDxcHNXOHBvFQ6zrmTksIIe5IGiAhRJnl6w0sijrB/3acAqCpjzsrQoNpUNPVzJmVTG/Qs/PcTg6mH6SfoZ/cCkMIGyYNkBCiTBJTs5m4Job9Z68D8ESnerw+sBmOGsub8rpdTn4OIV+FADAhfwKOWkczZySEMBdpgIQQpfbrscu8/HUc17N0uGntmfdoEINa+po7LSGEKDNpgIQQd6TTG3j35+N8tOs0AEF1PFgeGox/DRczZyaEEHdHGiAhRIkuXs/ixTUxxJy/AcBTXQIIGxCI1t7yp7yEEKI4duZOoMC8efNQqVRMnjy52JinnnoKlUpV6Kt58+bGmPDw8CJjcnJyKqEKIazL1sNJDFj6GzHnb+DuaM/KJ9oyc0hzaX6EEFWeRewB2r9/Px999BEtW7YsMW7p0qXMnz/f+Dg/P59WrVrx2GOPmcS5u7tz/Phxk2WOjnKwoxCllW+AOZHH+GzPeQBa+XmyfGQwftWdzZyZEEKUD7M3QBkZGYwaNYqPP/6YOXPmlBjr4eGBh4eH8fF3333H9evXGTt2rEmcSqXC29u7QvIVwtqdv5bFkkNqLmTebH6e7VafV/oF4mBvMTuMhRDinpm9ARo/fjwDBw6kT58+d2yAbrdq1Sr69OmDv7+/yfKMjAz8/f3R6/W0bt2a2bNnExwcXOw4ubm55ObmGh+npaUBoNPp0Ol0ZcrpTgrGK+9xLYW11wfWXeOWQ0nM+O4wGbkqPJzsWTC0Bb0Da4GiR6fTmzu9e2eAOT3mEB8fDwbr3IZg3e9RkPqsQUXVWJbxVIqiKOX66mWwdu1a/vvf/7J//34cHR3p2bMnrVu3ZsmSJXdcNzExET8/PyIiIhg+fLhx+d69ezl58iRBQUGkpaWxdOlSIiMjiYuLo1GjRkWONXPmTGbNmlVoeUREBM7OsstfWD+dAb47a8fuyzf38tR3UxjTSE81rZkTE0KIMsjKyiI0NJTU1FTc3d1LjDVbA3ThwgXatWvH1q1badWqFUCZGqB58+bx3nvvcenSJRwcir+pocFgoE2bNnTv3p1ly5YVGVPUHiA/Pz9SUlLu+AMsK51OR1RUFCEhIWg01ncVWmuvD6yvxrNXM5m07gBHEtMBeKZrPZrln6Z/P+uo73bWtv2KYu01Sn1VX0XVmJaWhpeXV6kaILNNgf39998kJyfTtm1b4zK9Xs+uXbtYvnw5ubm5qNVFn2miKAqffvopo0ePLrH5AbCzs6N9+/Y3d3kXQ6vVotUW/ldXo9FU2JuvIse2BNZeH1hHjd/HXSJs/QEy8/RUd3Fg0fBWdG1QjcjI01ZR3+30Bj1xl+KIz4qnn7qf1dV3O2vchreS+qq+8q6xLGOZrQHq3bs3Bw8eNFk2duxYAgMDefXVV4ttfgB27tzJyZMnGTdu3B1fR1EUYmNjCQoKuuechbAWOTo9s344wpo/bx7o3KF+dZY9Hoy3h6NVH3eQk59Dl/AuADyT/4zcCkMIG2a2BsjNzY0WLVqYLHNxcaFGjRrG5WFhYSQkJPD555+bxK1atYqOHTsWWh9g1qxZdOrUiUaNGpGWlsayZcuIjY1lxYoVFVeMEFXIyeQMJkREcywpHZUKXux1HxN7N8JeLWd5CSFsh9nPAitJYmIi58+fN1mWmprK+vXrWbp0aZHr3Lhxg+eee46kpCQ8PDwIDg5m165ddOjQoTJSFsKirf/7Iq9/d4hsnR4vVy1LRrTm/kZe5k5LCCEqnUU1QDt27DB5HB4eXijGw8ODrKysYsdYvHgxixcvLufMhKjasvLyeXPTYb79+yIAXRrWYMnjranlJlNAQgjbZFENkBCi/J24nM74r6KJT87ATgWT+zRmfK/7UNupzJ2aEEKYjTRAQlgpRVH45q+LvPn9IXJ0Bmq5aVn6eDCdG9Ywd2pCCGF20gAJYYUyc/N5beNBvou9BEC3Rl4sHtEaL1e5sqEQQoA0QEJYnSOX0pgQEc3plEzUdipe7tuY57s3xE6mvNCoNbx+/+vEx8ejUVv39VWEECWTBkgIK6EoChF/nmfWD0fIyzfg4+HIspHBtA+obu7ULIaD2oE3u79JZEYkDuqSL6IqhLBu0gAJYQXSc3SEbTjI5gOJADwQWIv3HmtFNRf5Iy+EEEWRBkiIKu5QQirjI6I5dzULezsVr/YPZNz99WXKqwgGxcDhK4c5n30eg2IwdzpCCDOSBkiIKkpRFD7fc47//niUPL2BOp5OvB8aTJt61cydmsXK1mUT/HEwAKN1o9E6yEHhQtgqaYCEqIJSs3W8+u0BfjqcBEDfZrV5d1grPJzlwF4hhCgNaYCEqGJiL9xgQkQ0F69no1GrmDGgKU91CUClkikvIYQoLWmAhKgiFEVh1e4zLPjpGDq9Qr3qziwPDaZlXU9zpyaEEFWONEBCVAE3svKY+k0c244mAzAgyJv5j7bE3VGmvIQQ4m5IAySEhfv73DVejIjhUmoODvZ2vDGoGU90rCdTXkIIcQ+kARLCQhkMCh/9dpp3fz6O3qBQ38uF5aHBNPf1MHdqQghR5UkDJIQFupqRy8vfxLHj+BUAhrTyZe7QIFy18it7LzRqDVM6TuH06dNyKwwhbJx8mgphYf48c40X10RzOS0Xrb0ds4Y0Z0R7P5nyKgcOagfm955PZK7cCkMIWycNkBAWwmBQ+N+OkyyKOoFBgYY1XVgxqg2B3u7mTk0IIayONEBCWIAr6blM+TqW3+JTABjapg6zH2qBi0x5lSuDYuDsjbNczr0st8IQwsbJp6sQZvbHyRQmrYvlSnouTho1bz/UnMfa+Zk7LauUrcum8f8aAzB84HC5FYYQNkwaICHMRG9QWPZLPMt+jUdRoHFtV1aEtqFRbTdzpyaEEFZPGiAhzCA5LYeJa2PYe/oaACPa+TFzSHOcHNRmzkwIIWyDNEBCVLJdJ67w0rpYrmbm4eygZu4jQTwcXMfcaQkhhE2RBkiISpKvN7B42wn+t+MUigJNfdxZERpMg5qu5k5NCCFsjjRAQlSCxNRsJq2J5c+zN6e8RnWsxxuDmuGokSkvIYQwB2mAhKhg248lM+XrWK5n6XDV2jP/0SAGtfQ1d1pCCGHTpAESooLo9AYW/nycD3edBqBFHXdWhLbBv4aLmTOzXfZ29jzf5nnOnT+HvZ18/Alhy+QTQIgKkHAjmxcjook+fwOAp7oEEDYgEK29THmZk9Zey7L+y4iMjERrL9cAEsKWSQMkRDmLOnKZqd/EkZqtw83RnneHtaR/Cx9zpyWEEOIW0gAJUU7y8g3M33KMT38/A0ArP0+WjwzGr7qzmTMTBRRF4UrmFVLzU1EUxdzpCCHMSBogIcrBhWtZTIiIJu5iKgDP3F+faf0DcbC3M3Nm4lZZuizqLL15zaUh/Yfg4CB3hBfCVkkDJMQ92nIwkWnrD5Cek4+Hk4b3HmtFn2a1zZ2WEEKIEljMv6fz5s1DpVIxefLkYmN27NiBSqUq9HXs2DGTuPXr19OsWTO0Wi3NmjVj48aNFZy9sEW5Oj1vbjrE/30VTXpOPm39qxE5qZs0P0IIUQVYxB6g/fv389FHH9GyZctSxR8/fhx3d3fj45o1axq/37NnDyNGjGD27Nk88sgjbNy4keHDh7N79246duxY7rkL23QlG4Z//CdHEtMBeL5HQ17u2xiN2mL+pxBCCFECs39aZ2RkMGrUKD7++GOqVatWqnVq1aqFt7e38Uut/vfU4iVLlhASEkJYWBiBgYGEhYXRu3dvlixZUkEVCFuz+UAi7x5UcyQxneouDoSPbc/0BwOl+RFCiCrE7HuAxo8fz8CBA+nTpw9z5swp1TrBwcHk5OTQrFkzXn/9dXr16mV8bs+ePbz00ksm8f369SuxAcrNzSU3N9f4OC0tDQCdTodOpytDNXdWMF55j2sprLm+HJ2eOZHHWffXRUBFu3oeLB7RCm93R6uq15q34a01VcTvt6Ww5m0IUp81qKgayzKeWRugtWvXEh0dzf79+0sV7+Pjw0cffUTbtm3Jzc3liy++oHfv3uzYsYPu3bsDkJSURO3apsdg1K5dm6SkpGLHnTdvHrNmzSq0fOvWrTg7V8wpzFFRURUyrqWwtvouZ0P4CTWXslSoUAipo9Df9yrRu381d2oVxtq2IUCOPsf4/a+//oqj2tGM2VQ8a9yGt5L6qr7yrjErK6vUsWZrgC5cuMCkSZPYunUrjo6l+xBq0qQJTZo0MT7u3LkzFy5cYOHChcYGCEClUpmspyhKoWW3CgsLY8qUKcbHaWlp+Pn50bdvX5NjjcqDTqcjKiqKkJAQNBpNuY5tCayxvk2xl1jyw1Gy8vTUcHFgwSNNyTz1t1XVeCtr3IYFcvNzGWUYxaVLl+jbpy+uTq7mTqlCWPM2BKnPGlRUjQUzOKVhtgbo77//Jjk5mbZt2xqX6fV6du3axfLly8nNzTU5tqc4nTp14ssvvzQ+9vb2LrS3Jzk5udBeoVtptVq02sKXxddoNBX25qvIsS2BNdSXnXfzLK9v/r4IQJeGNVgyojXVnNREnrKOGktijfVpNBpWP7SayMhIXJ1cra6+21njNryV1Ff1lXeNZRnLbA1Q7969OXjwoMmysWPHEhgYyKuvvlqq5gcgJiYGH59/bzPQuXNnoqKiTI4D2rp1K126dCmfxIVNOHE5nfFfRROfnIGdCib1bsyEB+5Dbaey6nl5IYSwFWZrgNzc3GjRooXJMhcXF2rUqGFcHhYWRkJCAp9//jlw8wyvgIAAmjdvTl5eHl9++SXr169n/fr1xjEmTZpE9+7dWbBgAQ899BCbNm1i27Zt7N69u/KKE1WWoih88/dF3tx0iBydgVpuWpY+HkznhjXMnZooB4qikJmXSY4+R26FIYSNM/tZYCVJTEzk/Pnzxsd5eXlMnTqVhIQEnJycaN68OT/++CMDBgwwxnTp0oW1a9fy+uuv88Ybb9CwYUPWrVsn1wASd5SZm8/r3x1iY0wCAN0aebF4RGu8XOWu4dYiS5dFtYU3L7dxvd91uRWGEDbMohqgHTt2mDwODw83eTxt2jSmTZt2x3GGDRvGsGHDyjEzYe2OJqYxPiKa01cyUdupmBLSmP/r0RA7u+IPnhdCCFF1WVQDJERlUxSFNX9eYOYPh8nLN+Dt7sj7ocG0D6hu7tSEEEJUIGmAhM1Kz9ExY+Mhfoi7BMADgbVY+FgrqrvItIgQQlg7aYCETTqUkMqEiGjOXs3C3k7FtP5NeOb+BjLlJYQQNkIaIGFTFEXhi73nmLP5KHl6A3U8nXg/NJg29Up3HzohhBDWQRogYTNSs3VMX3+ALYduXigzpFlt3h3WEk9nmfISQghbIw2QsAlxF24wYU00F65lo1GrCHuwKWO7BpR4ixRhfdR2aoYGDiUpMQm1XekutiqEsE7SAAmrpigKn/5+lvlbjqLTK/hVd2L5yDa08vM0d2rCDBztHVk7dC2RkZE42lv3jVCFECWTBkhYrRtZeUz95gDbjl4GYECQN/MfbYm7o3XfW0cIIcSdSQMkrNLf564zcU0MCTeycVDb8cagpjzRyV+mvIQQQgDSAAkrYzAofPzbad79+Tj5BoWAGs4sD21Dizoe5k5NWIDMvExc57kCcL3PdTw1nuZNSAhhNtIACatxLTOPl7+OZfvxKwAMaeXL3KFBuGrlbS6EEMKU/GUQVuHPM9eYuCaGpLQctPZ2zBzSnMfb+8mUlxBCiCJJAySqNINB4YOdp1gUdQK9QaFBTRdWhLahqY+7uVMTQghhwaQBElVWSkYuL62L5bf4FACGBtdh9sMtcJEpLyGEEHcgfylElfTHqRQmrY3lSnoujho7Zj/Ugsfa+Zk7LSGEEFWENECiStEbFN7/NZ5lv8RjUKBxbVdWhLahUW03c6cmhBCiCpEGSFQZyWk5TF4Xyx+nrgIwop0fM4c0x8lBbmkgSkdtp+bBhg+SfCVZboUhhI2TBkhUCb/FX+GldbGkZOTh7KBm7iNBPBxcx9xpiSrG0d6RTSM2ya0whBDSAAnLlq83sGRbPCt2nERRINDbjRWj2tCwpqu5UxNCCFGFSQMkLFZiajaT1sTy59lrAIzqWI83BjXDUSNTF0IIIe6NNEDCIm0/nsyUdbFcz9LhqrVn3tAgBrfyNXdaoorLzMuk1sJa6PV6kvokya0whLBh0gAJi6LTG1i49Tgf7jwNQIs67iwf2YYALxczZyasRZYuy9wpCCEsgDRAwmIk3MjmxYhoos/fAOCpLgGEDQhEay9TXkIIIcqXNEDCIkQduczUb+JIzdbh5mjPu8Na0r+Fj7nTEkIIYaWkARJmlZdvYMFPx1i1+wwArep6sDy0DX7Vnc2cmRBCCGsmDZAwmwvXspiwJoa4CzcAeOb++kzrH4iDvZ15ExNCCGH1pAESZvHToURe+fYA6Tn5eDhpeO+xVvRpVtvcaQkhhLAR0gCJSpWbr2fuj0f5bM85ANrU8+T90DbU8XQyc2bCFtip7OherztXr17FTiV7GoWwZdIAiUpzNiWTCWuiOZSQBsB/ejRgat8maNTyh0hUDieNE9ue2EZkZCROGmm6hbBl0gCJSvFD3CXCNhwkIzef6i4OvDe8Fb2a1DJ3WkIIIWyUNECiQuXo9Ly9+QgR+84D0CGgOstGBuPtITeiFEIIYT4WM/cwb948VCoVkydPLjZmw4YNhISEULNmTdzd3encuTM///yzSUx4eDgqlarQV05OTgVXIG536koGD6/4nYh951Gp4MUH7iPi2Y7S/AizyczLxHexL08efJLMvExzpyOEMCOL2AO0f/9+PvroI1q2bFli3K5duwgJCWHu3Ll4enqyevVqBg8ezL59+wgODjbGubu7c/z4cZN1HR3lj25l2hR7iTd/OEpWnh4vVwcWj2hNt0Y1zZ2WEKRkp5g7BSGEBTB7A5SRkcGoUaP4+OOPmTNnTomxS5YsMXk8d+5cNm3axA8//GDSAKlUKry9vSsiXXEH2Xl6Ik7asW/PIQA6N6jB0sdbU8tdGlAhhBCWw+wN0Pjx4xk4cCB9+vS5YwN0O4PBQHp6OtWrVzdZnpGRgb+/P3q9ntatWzN79myTBul2ubm55ObmGh+npd08S0mn06HT6cqU050UjFfe41qC+OQMJq6N4+QVO1TAi70a8kLPBqjtVFZVrzVvQ7Du+m6tqSJ+vy2FNW9DkPqsQUXVWJbxzNoArV27lujoaPbv339X67/33ntkZmYyfPhw47LAwEDCw8MJCgoiLS2NpUuX0rVrV+Li4mjUqFGR48ybN49Zs2YVWr5161acnSvmlgxRUVEVMq657EtW8c0ZO3QGFe4ahScbGWiYc5yffzp+55WrKGvbhrezxvpy9P8eC/jrr7/iqLbuPZPWuA1vJfVVfeVdY1ZWVqljVYqiKOX66qV04cIF2rVrx9atW2nVqhUAPXv2pHXr1oWmuoqyZs0annnmGTZt2kSfPn2KjTMYDLRp04bu3buzbNmyImOK2gPk5+dHSkoK7u7uZSvsDnQ6HVFRUYSEhKDRaMp1bHPIzM1n1uajbIxNBKBrg2o8WP0KQwdYR31FsbZteDtrri8zL5NqC6sBkDwpGU8XT/MmVEGseRuC1GcNKqrGtLQ0vLy8SE1NvePfb7PtAfr7779JTk6mbdu2xmV6vZ5du3axfPlycnNzUavVRa67bt06xo0bxzfffFNi8wNgZ2dH+/btiY+PLzZGq9Wi1WoLLddoNBX25qvIsSvLsaQ0xn8Vzakrmdip4OW+TXimSz1++mmLVdR3J9ZeozXWp1H+rcca67udtdco9VV95V1jWcYyWwPUu3dvDh48aLJs7NixBAYG8uqrrxbb/KxZs4ann36aNWvWMHDgwDu+jqIoxMbGEhQUVC55i5s/07X7LzDz+8Pk5hvwdndk2chgOtSvbtVz1qLqs1PZ0danLak3UuVWGELYOLM1QG5ubrRo0cJkmYuLCzVq1DAuDwsLIyEhgc8//xy42fw8+eSTLF26lE6dOpGUlASAk5MTHh4eAMyaNYtOnTrRqFEj0tLSWLZsGbGxsaxYsaISq7Ne6Tk6Zmw8xA9xlwDo1aQm7w1vTXUXBzNnJsSdOWmc2DN2j9wKQwhhORdCLEpiYiLnz583Pv7www/Jz89n/Pjx+Pj4GL8mTZpkjLlx4wbPPfccTZs2pW/fviQkJLBr1y46dOhgjhKsyqGEVAa/v5sf4i5hb6ci7MFAVo1pL82PEEKIKsfsp8HfaseOHSaPw8PDS3y+KIsXL2bx4sXll5RAURS+3HuO2ZuPkqc3UMfTiWUjg2nrX83cqQkhhBB3xaIaIGF50nJ0TF9/gMiDN6cb+zStzcLHWuLpLHt9RNWTpcui2YpmZGVlER8Sj4fGw9wpCSHMRBogUay4CzeYsCaaC9ey0ahVTH+wKU93DUClUpk7NSHuiqIonEs9Z/xeCGG7pAEShSiKwurfzzJvy1F0egW/6k4sH9mGVn6e5k5NCCGEKBfSAAkTN7LyeOXbA0QduQzAgy28mf9oSzycrPtaFEIIIWyLNEDCKPr8dV6MiCHhRjYOajteH9SU0Z38ZcpLCCGE1ZEGSGAwKHyy+zTv/HScfINCQA1nloe2oUUdOUBUCCGEdZIGyMZdy8xj6jdx/HosGYDBrXyZ+0gL3BxlyksIIYT1kgbIhu0/e42Ja2JITM1Ba2/HW4ObM7KDn0x5CaulUqlo6tWUjIwMeZ8LYeOkAbJBBoPCBztPsSjqBHqDQoOaLqwIbUNTn5LvnCtEVeescSbuuTgiIyNx1jibOx0hhBlJA2RjUjJyeWldLL/FpwAwNLgOsx9ugYtW3gpCCCFsh/zVsyF7Tl1l0toYktNzcdTY8fZDLXisbV2ZChBCCGFzpAGyAXqDwvJfT7L0lxMYFGhUy5UVo9rQuLabuVMTolJl6bJo91E7MjIy6BnSU26FIYQNkwbIyiWn5zB5bSx/nLoKwPB2dZk1pAVODmozZyZE5VMUhaMpR43fCyFslzRAVmx3fAqT18WQkpGHs4Oa/z7SgkeC65o7LSGEEMLspAGyQvl6A0t/iWf59pMoCgR6u7E8tA331XI1d2pCCCGERZAGyMokpeYwcW0Mf565BkBox3q8OagZjhqZ8hJCCCEKSANkRXYcT2bK13Fcy8zDVWvP3KFBDGnla+60hBBCCIsjDZAV0OkNvLf1BCt3ngKgua87K0LbEODlYubMhBBCCMskDVAVl3Ajm4lrYvj73HUAxnT2J2xAU5nyEqIIKpUKfw9/srKy5PpXQtg4aYCqsG1HLjP12zhuZOlwc7TnnUdb8mCQj7nTEsJiOWuciR8fL7fCEEJIA1QV5eUbeOenY3yy+wwArep68P7INtSrIR/oQgghRGlIA1TFXLiWxYQ1McRduAHAuPvr82r/QBzs7cybmBBCCFGFSANUhfx0KIlXvo0jPScfDycNCx9rRUiz2uZOS4gqI1uXTbfV3Ui9kUqvkF5oNBpzpySEMBNpgKqA3Hw98yKPEf7HWQDa1PNk2chg6laTKS8hysKgGPg78W/j90II2yUNkIU7dzWTCRExHExIBeA/PRowtW8TNGqZ8hJCCCHuljRAFmzzgUtMX3+QjNx8qjlrWDS8Nb0Ca5k7LSGEEKLKkwbIAuXo9MzefISv9p0HoH1ANZaNDMbHw8nMmQkhhBDWQRogC3P6SgbjI2I4mpiGSgXje97H5D6NsJcpLyGEEKLcSANkQb6LSWDGxoNk5emp4eLAksdb061RTXOnJYQQQlgdaYAsQHaenpnfH2bdXxcA6NygBksfb00td0czZyaE9fFy8iIvL8/caQghzEwaIDOLv5zO+IhoTlzOQKWCSb0b8eIDjVDbyX2KhChvLg4uXHrpEpGRkbg4yM2ChbBlFnNgybx581CpVEyePLnEuJ07d9K2bVscHR1p0KABK1euLBSzfv16mjVrhlarpVmzZmzcuLGCsr433/x1gSHLf+fE5Qxqumn56pmOTO7TWJofIYQQooJZRAO0f/9+PvroI1q2bFli3JkzZxgwYADdunUjJiaGGTNmMHHiRNavX2+M2bNnDyNGjGD06NHExcUxevRohg8fzr59+yq6jFLL1cO09Qd55dsDZOv0dGvkReTEbnRp6GXu1IQQQgibYPYpsIyMDEaNGsXHH3/MnDlzSoxduXIl9erVY8mSJQA0bdqUv/76i4ULF/Loo48CsGTJEkJCQggLCwMgLCyMnTt3smTJEtasWVOhtZTG8aR03juo5nJ2InYqeLlvE/6vR0PsZK+PEBUuW5dN/y/7c/XqVXrp5FYYQtgyszdA48ePZ+DAgfTp0+eODdCePXvo27evybJ+/fqxatUqdDodGo2GPXv28NJLLxWKKWiaipKbm0tubq7xcVpaGgA6nQ6dTlfGior3y9FkJn19gNx8FbXdtCwe3pL2AdXQ6/PR68vtZcyq4OdVnj83S2PtNVpzfbl5uew6v8v4vU5jfTWCdW9DkPqsQUXVWJbxzNoArV27lujoaPbv31+q+KSkJGrXNr35Z+3atcnPzyclJQUfH59iY5KSkoodd968ecyaNavQ8q1bt+LsXH7327qWC2pFTVNPhSfuy+TKkT1EHim34S1KVFSUuVOocNZeozXWl6PPMX7/66+/4qi27jMtrXEb3krqq/rKu8asrKxSx5qtAbpw4QKTJk1i69atODqW/kNIpTKdKlIUpdDyomJuX3arsLAwpkyZYnyclpaGn58fffv2xd3dvdS5lUbHzqkc//t3+vUNscrd7zqdjqioKEJCrLM+sP4arbm+zLxMOHjz+wceeABPF0+z5lNRrHkbgtRnDSqqxoIZnNIwWwP0999/k5ycTNu2bY3L9Ho9u3btYvny5eTm5qJWq03W8fb2LrQnJzk5GXt7e2rUqFFizO17hW6l1WrRarWFlms0mnJ/8zXy9iBeVTFjWxJrrw+sv0ZrrE+j/FuPNdZ3O2uvUeqr+sq7xrKMZbazwHr37s3BgweJjY01frVr145Ro0YRGxtbqPkB6Ny5c6HdZVu3bqVdu3bGoouL6dKlS8UVI4QQQogqxWx7gNzc3GjRooXJMhcXF2rUqGFcHhYWRkJCAp9//jkAzz//PMuXL2fKlCk8++yz7Nmzh1WrVpmc3TVp0iS6d+/OggULeOihh9i0aRPbtm1j9+7dlVecEEIIISyaRVwHqDiJiYmcP3/e+Lh+/fpERkayY8cOWrduzezZs1m2bJnxFHiALl26sHbtWlavXk3Lli0JDw9n3bp1dOzY0RwlCCEsjLPGGa1d4SlvIYRtMftp8LfasWOHyePw8PBCMT169CA6OrrEcYYNG8awYcPKMTMhhDVwcXDhxis35FYYQgjL3gMkhBBCCFERpAESQgghhM2xqCkwIYSoSDn5OQxdN5TkK8k8kP+A1Z9iLIQonjRAQgiboTfo2XJqi/F7IYTtkikwIYQQQtgcaYCEEEIIYXOkARJCCCGEzZEGSAghhBA2RxogIYQQQtgcOQusCIqiAJCWllbuY+t0OrKyskhLS7PKU3CtvT6w/hqtub7MvEzIufl9Wloadnrr/B/QmrchSH3WoKJqLPi7XfB3vCQqpTRRNubixYv4+fmZOw0hhBBC3IULFy5Qt27dEmOkASqCwWDg0qVLuLm5oVKpynXstLQ0/Pz8uHDhAu7u7uU6tiWw9vrA+muU+qo+a69R6qv6KqpGRVFIT0/H19cXO7uS9/DKFFgR7Ozs7tg53it3d3erfWOD9dcH1l+j1Ff1WXuNUl/VVxE1enh4lCrOOifAhRBCCCFKIA2QEEIIIWyONECVTKvV8tZbb6HVas2dSoWw9vrA+muU+qo+a69R6qv6LKFGOQhaCCGEEDZH9gAJIYQQwuZIAySEEEIImyMNkBBCCCFsjjRAQgghhLA50gCVo/z8fF5//XXq16+Pk5MTDRo04O2338ZgMJS43s6dO2nbti2Ojo40aNCAlStXVlLGZXM39e3YsQOVSlXo69ixY5WYeemlp6czefJk/P39cXJyokuXLuzfv7/EdarK9itQ1hoteRvu2rWLwYMH4+vri0ql4rvvvjN5XlEUZs6cia+vL05OTvTs2ZPDhw/fcdz169fTrFkztFotzZo1Y+PGjRVUwZ1VRI3h4eFFbtOcnJwKrKRod6pvw4YN9OvXDy8vL1QqFbGxsaUa11K2YUXUZ0nbD0quUafT8eqrrxIUFISLiwu+vr48+eSTXLp06Y7jVvQ2lAaoHC1YsICVK1eyfPlyjh49yjvvvMO7777L+++/X+w6Z86cYcCAAXTr1o2YmBhmzJjBxIkTWb9+fSVmXjp3U1+B48ePk5iYaPxq1KhRJWRcds888wxRUVF88cUXHDx4kL59+9KnTx8SEhKKjK9K269AWWssYInbMDMzk1atWrF8+fIin3/nnXdYtGgRy5cvZ//+/Xh7exMSEkJ6enqxY+7Zs4cRI0YwevRo4uLiGD16NMOHD2ffvn0VVUaJKqJGuHkF3lu3Z2JiIo6OjhVRQonuVF9mZiZdu3Zl/vz5pR7TkrZhRdQHlrP9oOQas7KyiI6O5o033iA6OpoNGzZw4sQJhgwZUuKYlbINFVFuBg4cqDz99NMmy4YOHao88cQTxa4zbdo0JTAw0GTZf/7zH6VTp04VkuO9uJv6tm/frgDK9evXKzi7e5eVlaWo1Wpl8+bNJstbtWqlvPbaa0WuU5W2n6LcXY1VZRsCysaNG42PDQaD4u3trcyfP9+4LCcnR/Hw8FBWrlxZ7DjDhw9X+vfvb7KsX79+yuOPP17uOZdVedW4evVqxcPDowIzvTu313erM2fOKIASExNzx3EsdRuWV32Wuv0UpeQaC/z5558KoJw7d67YmMrYhrIHqBzdf//9/PLLL5w4cQKAuLg4du/ezYABA4pdZ8+ePfTt29dkWb9+/fjrr7/Q6XQVmm9Z3U19BYKDg/Hx8aF3795s3769olO9K/n5+ej1+kL/RTk5ObF79+4i16lK2w/ursYCVWEb3urMmTMkJSWZbB+tVkuPHj34448/il2vuG1a0jrmcrc1AmRkZODv70/dunUZNGgQMTExFZ1upalK2/BuVeXtl5qaikqlwtPTs9iYytiG0gCVo1dffZWRI0cSGBiIRqMhODiYyZMnM3LkyGLXSUpKonbt2ibLateuTX5+PikpKRWdcpncTX0+Pj589NFHrF+/ng0bNtCkSRN69+7Nrl27KjHz0nFzc6Nz587Mnj2bS5cuodfr+fLLL9m3bx+JiYlFrlOVth/cXY1VaRveKikpCaDI7VPwXHHrlXUdc7nbGgMDAwkPD+f7779nzZo1ODo60rVrV+Lj4ys038pSlbbh3ajK2y8nJ4fp06cTGhpa4k1QK2Mbyt3gy9G6dev48ssviYiIoHnz5sTGxjJ58mR8fX0ZM2ZMseupVCqTx8o/F+e+fbm53U19TZo0oUmTJsbHnTt35sKFCyxcuJDu3btXVuql9sUXX/D0009Tp04d1Go1bdq0ITQ0lOjo6GLXqSrbr0BZa6xq2/B2RW2fO22bu1nHnMqab6dOnejUqZPxcdeuXWnTpg3vv/8+y5Ytq7A8K1NV24ZlUVW3n06n4/HHH8dgMPC///3vjvEVvQ1lD1A5euWVV5g+fTqPP/44QUFBjB49mpdeeol58+YVu463t3ehjjY5ORl7e3tq1KhR0SmXyd3UV5ROnTpZ7H8qDRs2ZOfOnWRkZHDhwgX+/PNPdDod9evXLzK+Km2/AmWtsSiWvA0LeHt7AxS5fW7/z/L29cq6jrncbY23s7Ozo3379ha/TUurKm3D8lAVtp9Op2P48OGcOXOGqKioEvf+QOVsQ2mAylFWVhZ2dqY/UrVaXeJp4p07dyYqKspk2datW2nXrh0ajaZC8rxbd1NfUWJiYvDx8SnP1Mqdi4sLPj4+XL9+nZ9//pmHHnqoyLiqtP1uV9oai1IVtmH9+vXx9vY22T55eXns3LmTLl26FLtecdu0pHXM5W5rvJ2iKMTGxlr8Ni2tqrQNy4Olb7+C5ic+Pp5t27aV6p/DStmG5XY4tVDGjBmj1KlTR9m8ebNy5swZZcOGDYqXl5cybdo0Y8z06dOV0aNHGx+fPn1acXZ2Vl566SXlyJEjyqpVqxSNRqN8++235iihRHdT3+LFi5WNGzcqJ06cUA4dOqRMnz5dAZT169ebo4Q7+umnn5QtW7Yop0+fVrZu3aq0atVK6dChg5KXl6coStXefgXKWqMlb8P09HQlJiZGiYmJUQBl0aJFSkxMjPHskvnz5yseHh7Khg0blIMHDyojR45UfHx8lLS0NOMYo0ePVqZPn258/PvvvytqtVqZP3++cvToUWX+/PmKvb29snfv3kqvT1EqpsaZM2cqP/30k3Lq1CklJiZGGTt2rGJvb6/s27fP4uq7evWqEhMTo/z4448KoKxdu1aJiYlREhMTi63PkrZhRdRnSdtPUUquUafTKUOGDFHq1q2rxMbGKomJicav3Nxc4xjm2IbSAJWjtLQ0ZdKkSUq9evUUR0dHpUGDBsprr71mspHHjBmj9OjRw2S9HTt2KMHBwYqDg4MSEBCgfPDBB5WceencTX0LFixQGjZsqDg6OirVqlVT7r//fuXHH380Q/als27dOqVBgwaKg4OD4u3trYwfP165ceOG8fmqvP0KlLVGS96GBafo3/41ZswYRVFunib+1ltvKd7e3opWq1W6d++uHDx40GSMHj16GOMLfPPNN0qTJk0UjUajBAYGmrXZq4gaJ0+erNSrV09xcHBQatasqfTt21f5448/KrGqf92pvtWrVxf5/FtvvWUcw5K3YUXUZ0nbT1FKrrHg9P6ivrZv324cwxzbUKUo/xyxKYQQQghhI+QYICGEEELYHGmAhBBCCGFzpAESQgghhM2RBkgIIYQQNkcaICGEEELYHGmAhBBCCGFzpAESQgghhM2RBkgIIYQQNkcaICGEEELYHGmAhBBCCGFzpAESQtiEK1eu4O3tzdy5c43L9u3bh4ODA1u3bjVjZkIIc5B7gQkhbEZkZCQPP/wwf/zxB4GBgQQHBzNw4ECWLFli7tSEEJVMGiAhhE0ZP34827Zto3379sTFxbF//34cHR3NnZYQopJJAySEsCnZ2dm0aNGCCxcu8Ndff9GyZUtzpySEMAM5BkgIYVNOnz7NpUuXMBgMnDt3ztzpCCHMRPYACSFsRl5eHh06dKB169YEBgayaNEiDh48SO3atc2dmhCikkkDJISwGa+88grffvstcXFxuLq60qtXL9zc3Ni8ebO5UxNCVDKZAhNC2IQdO3awZMkSvvjiC9zd3bGzs+OLL75g9+7dfPDBB+ZOTwhRyWQPkBBCCCFsjuwBEkIIIYTNkQZICCGEEDZHGiAhhBBC2BxpgIQQQghhc6QBEkIIIYTNkQZICCGEEDZHGiAhhBBC2BxpgIQQQghhc6QBEkIIIYTNkQZICCGEEDZHGiAhhBBC2BxpgIQQQghhc/4feCT64X8eJGUAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(8, 12, 200)\n",
"y = x/2\n",
"\n",
"plt.plot(x, y, label=\"$f(x) = x/2$\")\n",
"plt.axhline(5, color=\"red\", linestyle=\"--\", label=\"Limit L = 5\")\n",
"plt.axvline(10, color=\"green\", linestyle=\"--\", label=\"x → 10\")\n",
"plt.legend()\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"f(x)\")\n",
"plt.grid(True)\n",
"plt.title(\"limit as x approaches 10\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "fd32134d",
"metadata": {},
"source": [
"### 1.1 Kinds of Limits \n",
"Note: this will not be covered during workshop time but is intended to be used as a reference"
]
},
{
"cell_type": "markdown",
"id": "888e46fe",
"metadata": {},
"source": [
"\n",
"1. **Two-sided limit** \n",
" $\\lim_{x \\to a} f(x) = L$\n",
" Requires $f(x)$ to approach the same $L$ from both the left ($x \\to a^-$) and the right ($x \\to a^+$).\n",
"\n",
"2. **One-sided limits** \n",
" - Left-hand limit: \n",
" $\\lim_{x \\to a^-} f(x) = L$\n",
" - Right-hand limit: \n",
" $\\lim_{x \\to a^+} f(x) = L$\n",
"\n",
"3. **Limits at infinity** \n",
" - $\\lim_{x \\to \\infty} f(x)$ \n",
" - $\\lim_{x \\to -\\infty} f(x)$ \n",
" Used to describe asymptotic behavior.\n",
"\n",
"4. **Infinite limits** \n",
" - $\\lim_{x \\to a} f(x) = \\infty$ \n",
" Means $f(x)$ grows without bound as $x$ approaches $a$.\n",
"\n",
"\n",
"\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "7907ea81",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 2, figsize=(12, 9))\n",
"\n",
"# two-sided limit:\n",
"ax = axes[0, 0]\n",
"a = 1.0\n",
"x = np.linspace(0, 2, 600)\n",
"y = (x**2 - 1) / (x - 1) # equals x+1 for x != 1\n",
"y[np.isclose(x, a, atol=1e-6)] = np.nan # hide the undefined point\n",
"ax.plot(x, y, label=r\"$f(x)=\\frac{x^2-1}{x-1}$\")\n",
"ax.axvline(a, linestyle=\"--\") # approach point\n",
"ax.axhline(2, linestyle=\"--\") # limit value\n",
"ax.scatter([a], [2], facecolors=\"none\", edgecolors=\"red\", s=80, zorder=3,\n",
" label=\"removable discontinuity\")\n",
"ax.set_title(\"Two-sided limit: $\\\\lim_{x\\\\to 1} f(x) = 2$\")\n",
"ax.grid(True)\n",
"ax.legend(loc=\"best\")\n",
"\n",
"# one-sided limits: step (different left/right limits at a=0)\n",
"ax = axes[0, 1]\n",
"a = 0.0\n",
"x = np.linspace(-4, 4, 801)\n",
"f = np.where(x < 0, 0.0, 1.0)\n",
"ax.plot(x, f, label=\"f(x) = 0 for x<0; 1 for x ≥ 0\")\n",
"ax.axvline(a, linestyle=\"--\")\n",
"ax.axhline(0, linestyle=\"--\", label=r\"$L^- = 0$\")\n",
"ax.axhline(1, linestyle=\"--\", label=r\"$L^+ = 1$\")\n",
"ax.set_title(\"One-sided limits at $a=0$ (no two-sided limit)\")\n",
"ax.grid(True)\n",
"ax.legend(loc=\"best\")\n",
"\n",
"# limits at infinity- horizontal asymptote\n",
"ax = axes[1, 0]\n",
"x = np.linspace(-10, 10, 1201)\n",
"f = (2*x**2 + 1) / (x**2 + 1)\n",
"ax.plot(x, f, label=r\"$f(x)=\\frac{2x^2+1}{x^2+1}$\")\n",
"ax.axhline(2, linestyle=\"--\", label=\"asymptote y=2\")\n",
"ax.set_title(r\"Limits at infinity: $\\lim_{x\\to\\pm\\infty} f(x)=2$\")\n",
"ax.grid(True)\n",
"ax.legend(loc=\"best\")\n",
"\n",
"# infinite limit at a point: vertical asymptote\n",
"# f(x) = 1/(x-2)^2 -> +∞ as x -> 2\n",
"ax = axes[1, 1]\n",
"a = 2.0\n",
"\n",
"x_left = np.linspace(0.5, 1.95, 400)\n",
"x_right = np.linspace(2.05, 3.5, 400)\n",
"f_left = 1.0 / (x_left - a)**2\n",
"f_right = 1.0 / (x_right - a)**2\n",
"ax.plot(x_left, f_left)\n",
"ax.plot(x_right, f_right, label=r\"$f(x)=\\frac{1}{(x-2)^2}$\")\n",
"ax.axvline(a, linestyle=\"--\") # vertical asymptote\n",
"ax.set_ylim(0, min(50, max(f_left.max(), f_right.max()))) # keep plot readable\n",
"ax.set_title(r\"Infinite limit: $\\lim_{x\\to 2} \\frac{1}{(x-2)^2}=+\\infty$\")\n",
"ax.grid(True)\n",
"ax.legend(loc=\"best\")\n",
"\n",
"for ax in axes[1, :]:\n",
" ax.set_xlabel(\"x\")\n",
"for ax in axes[:, 0]:\n",
" ax.set_ylabel(\"y\")\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "59bc64fc",
"metadata": {},
"source": [
"## 2 | Derivatives\n",
"\n",
"The derivative represents the *instantaneous rate of change* of a function.\n",
"\n",
"- **Secant slope** = average rate of change between two points.\n",
"- **Tangent slope** = instantaneous rate of change.\n",
"\n",
"Definition of derivative:\n",
"\n",
"$$f'(x) = \\lim_{h \\to 0}\\frac{f(x+h) - f(x)}{h}$$"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "4538025f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"#import ipywidgets as widgets\n",
"\n",
"f = lambda x: x**2\n",
"df = lambda x: 2*x\n",
"\n",
"x = np.linspace(-5, 5, 400)\n",
"y = f(x)\n",
"\n",
"#@widgets.interact(x0=(-4.0, 4.0, 0.1))\n",
"#def tangent_plot(x0=1):\n",
"plt.figure(figsize=(6,4))\n",
"plt.plot(x, y, label=\"$f(x) = x^2$\")\n",
"plt.scatter([x0], [f(x0)], color=\"red\")\n",
"plt.ylim(0,25)\n",
"plt.title(f\"Point of tangency at x={x0}, f({x0})={f(x0)}\")\n",
"\n",
"# tangent line\n",
"slope = df(x0)\n",
"tangent = slope*(x - x0) + f(x0)\n",
"plt.plot(x, tangent, \"--\", label=f\"Tangent at x={x0}, slope={slope:.2f}\")\n",
"plt.ylim(0, 25)\n",
"\n",
"plt.legend()\n",
"plt.grid(True)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "19baa061",
"metadata": {},
"source": [
"### 2.1 Derivative Rules Cheat Sheet"
]
},
{
"cell_type": "markdown",
"id": "54fdab7c",
"metadata": {},
"source": [
"- Power Rule: $\\frac{d}{dx}[x^n] = nx^{n-1}$\n",
"- Constant Rule: $\\frac{d}{dx}[c] = 0$\n",
"- Sum Rule: $\\frac{d}{dx}[f+g] = f' + g'$\n",
"- Product Rule: $\\frac{d}{dx}[fg] = f'g + fg'$\n",
"- Quotient Rule: $\\frac{d}{dx}\\left[\\frac{f}{g}\\right] = \\frac{f'g - fg'}{g^2}$\n",
"- Chain Rule: $\\frac{d}{dx}[f(g(x))] = f'(g(x)) \\cdot g'(x)$\n",
"- Exponential: $\\frac{d}{dx}[e^x] = e^x$, $\\;\\;\\frac{d}{dx}[a^x] = a^x\\ln(a)$\n",
"- Logarithm: $\\frac{d}{dx}[\\ln(x)] = \\frac{1}{x}$\n",
"- Trigonometric: \n",
" $\\frac{d}{dx}[\\sin(x)] = \\cos(x)$, \n",
" $\\frac{d}{dx}[\\cos(x)] = -\\sin(x)$, \n",
" $\\frac{d}{dx}[\\tan(x)] = \\sec^2(x)$\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "90c389f7",
"metadata": {},
"source": [
"### 2.2 Useful Derivatives\n",
"\n",
"$\\frac{d}{dx}(x) = 1$\n",
"\n",
"$\\frac{d}{dx}(\\sin x) = \\cos x$\n",
"\n",
"$\\frac{d}{dx}(\\cos x) = -\\sin x$\n",
"\n",
"$\\frac{d}{dx}(\\tan x) = \\sec^2 x$\n",
"\n",
"$\\frac{d}{dx}(\\cot x) = -\\csc^2 x$\n",
"\n",
"$\\frac{d}{dx}(\\sec x) = \\sec x \\tan x$\n",
"\n",
"$\\frac{d}{dx}(\\csc x) = -\\csc x \\cot x$\n",
"\n",
"$\\frac{d}{dx}(\\sin^{-1} x) = \\frac{1}{\\sqrt{1-x^2}}$\n",
"\n",
"$\\frac{d}{dx}(\\cos^{-1} x) = -\\frac{1}{\\sqrt{1-x^2}}$\n",
"\n",
"$\\frac{d}{dx}(\\tan^{-1} x) = \\frac{1}{1+x^2}$\n",
"\n",
"$\\frac{d}{dx}(\\ln(x)) = \\frac{1}{x}, \\; x > 0$\n",
"\n",
"$\\frac{d}{dx}(\\ln|x|) = \\frac{1}{x}, \\; x \\neq 0$\n",
"\n",
"$\\frac{d}{dx}(\\log_a(x)) = \\frac{1}{x \\ln(a)}, \\; x > 0$\n",
"\n",
"$\\frac{d}{dx}(e^x) = e^x$\n",
"\n",
"$\\frac{d}{dx}(a^x) = a^x \\ln(a)$"
]
},
{
"cell_type": "markdown",
"id": "82d7ff78",
"metadata": {},
"source": [
"### 2.3 Derivative Notation"
]
},
{
"cell_type": "markdown",
"id": "e2cc0785",
"metadata": {},
"source": [
"\n",
"There are several common notations for derivatives:\n",
"\n",
"| Notation Type | Example | Context |\n",
"|----------------|---------------|--------------------------------|\n",
"| Lagrange | $f'(x), f''(x)$ | General functions |\n",
"| Leibniz | $\\frac{dy}{dx}, \\frac{d^2y}{dx^2}$ | Differential equations, rigor |\n",
"| Newton | $\\dot{y}, \\ddot{y}$ | Physics, time derivatives |\n",
"| Euler | $Df(x)$ | Operator form |\n",
"| Partial | $\\frac{\\partial f}{\\partial x} , \\frac{\\partial^2 f}{\\partial x^2}$| Multivariable calculus |"
]
},
{
"cell_type": "markdown",
"id": "49f3c5c2",
"metadata": {},
"source": [
"## Practice Problems"
]
},
{
"cell_type": "markdown",
"id": "4abcdbd2",
"metadata": {},
"source": [
"Using the derivative rules (power, product, quotient, chain, exponential, logarithmic, trigonometric), solve the following:\n"
]
},
{
"cell_type": "markdown",
"id": "f647df48",
"metadata": {},
"source": [
"### 1. What is the instantaneous rate of change at $x=2$ of $f(x)=\\frac{x^2-2}{x-1}$"
]
},
{
"cell_type": "markdown",
"id": "c65fe8f8",
"metadata": {},
"source": [
"##### solution:"
]
},
{
"cell_type": "markdown",
"id": "0e3f2028",
"metadata": {},
"source": [
"Steps\n",
"\n",
"- Use the quotient rule: if $f=\\dfrac{u}{v}$ then $f'=\\dfrac{u'v-uv'}{v^2}$ with $u=x^2-2$, $v=x-1$.\n",
"\n",
"- Compute $u'=2x$, $v'=1$.\n",
"\n",
"- Substitute and simplify, then evaluate at $x=2$.\n",
"\n",
"- Work\n",
"$,f'(x)=\\dfrac{(2x)(x-1)-(x^2-2)(1)}{(x-1)^2}\n",
"=\\dfrac{x^2-2x+2}{(x-1)^2}.$\n",
"So $,f'(2)=\\dfrac{4-4+2}{1}=2.$"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "6bcc3452",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f'(2) ≈ 1.9990007500003912\n"
]
}
],
"source": [
"x = np.linspace(1.5, 2.5, 1000)\n",
"f = (x**2 - 2) / (x - 1)\n",
"\n",
"# compute derivative\n",
"dfdx = np.gradient(f, x) \n",
"\n",
"# solve at x=2\n",
"x0 = 2.0\n",
"idx = (np.abs(x - x0)).argmin() \n",
"print(\"f'(2) ≈\", dfdx[idx])"
]
},
{
"cell_type": "markdown",
"id": "c2f1a7e8",
"metadata": {},
"source": [
"#### 2. What is the derivative on $sin(e^{-x})$?"
]
},
{
"cell_type": "markdown",
"id": "51cc4cc5",
"metadata": {},
"source": [
"##### solution:"
]
},
{
"cell_type": "markdown",
"id": "d89b9e76",
"metadata": {},
"source": [
"- Let $u=e^{-x}$. Use the chain rule: $(\\sin u)'=\\cos u\\cdot u'$.\n",
"\n",
"- Compute $u'=-e^{-x}$."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "1ba69a32",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(x) = sin(exp(-x))\n",
"f'(x) = -exp(-x)*cos(exp(-x))\n"
]
}
],
"source": [
"x = sp.symbols('x')\n",
"f = sp.sin(sp.exp(-x))\n",
"dfdx = sp.diff(f, x)\n",
"print(\"f(x) = \", f)\n",
"print(\"f'(x) =\", dfdx)"
]
},
{
"cell_type": "markdown",
"id": "63912cf5",
"metadata": {},
"source": [
"#### 3. What is the derivative of $ \\frac{d^2}{dx^2} e^{ix}$, where $i=\\sqrt{-1}$?"
]
},
{
"cell_type": "markdown",
"id": "b036c46f",
"metadata": {},
"source": [
"##### solution:"
]
},
{
"cell_type": "markdown",
"id": "1d91aa36",
"metadata": {},
"source": [
"- First derivative by chain rule: $(e^{ix})'=i,e^{ix}$.\n",
"\n",
"- Differentiate again: $(i,e^{ix})'=i(i,e^{ix})=i^2 e^{ix}=-e^{ix}$."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "3280d677",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(x) = exp(I*x)\n",
"f '(x) = I*exp(I*x)\n",
"f''(x) = -exp(I*x)\n"
]
}
],
"source": [
"x = sp.symbols('x')\n",
"f = sp.exp(sp.I*x)\n",
"dfdx = sp.diff(f,x)\n",
"d2fx2 = sp.diff(dfdx,x)\n",
"\n",
"print(\"f(x) =\", f )\n",
"print(\"f '(x) =\", dfdx)\n",
"print(\"f''(x) =\", d2fx2)\n"
]
},
{
"cell_type": "markdown",
"id": "e84e89c1",
"metadata": {},
"source": [
"#### 4. What is the max acceleration on interval $ 0 \\le t \\le 3$ if a particle's position is given by $$ s(t) = t^3 - 3t^2 + 12t + 4?"
]
},
{
"cell_type": "markdown",
"id": "bfb720ef",
"metadata": {},
"source": [
"#### solution:"
]
},
{
"cell_type": "markdown",
"id": "81005ef9",
"metadata": {},
"source": [
"- Velocity: $v(t)=s'(t)=3t^2-6t+12$.\n",
"\n",
"- Acceleration: $a(t)=v'(t)=6t-6$.\n",
"\n",
"- To maximize $a$ on a closed interval, check critical points of $a$ (solve $a'(t)=0$) and the endpoints $t=0,3$.\n",
"\n",
"- Here $a'(t)=6>0$ (no interior extrema), so $a$ is increasing; max occurs at the right endpoint."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "ecef160f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Max acceleration on [0,3]: 12.0\n"
]
}
],
"source": [
"t = sp.symbols('t')\n",
"s = t**3 - 3*t**2 + 12*t + 4\n",
"\n",
"v = sp.diff(s, t)\n",
"a = sp.diff(v, t)\n",
"\n",
"s_func = sp.lambdify(t, s, 'numpy')\n",
"v_func = sp.lambdify(t, v, 'numpy')\n",
"a_func = sp.lambdify(t, a, 'numpy')\n",
"\n",
"t_vals = np.linspace(0, 3, 200)\n",
"s_vals = s_func(t_vals)\n",
"v_vals = v_func(t_vals)\n",
"a_vals = a_func(t_vals)\n",
"\n",
"max_accel = a_vals.max()\n",
"\n",
"print(\"Max acceleration on [0,3]:\", max_accel)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "47c75e5a",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"plt.plot(t_vals, s_vals, label=\"Position $s(t)$\")\n",
"plt.plot(t_vals, v_vals, label=\"Velocity $v(t)$\")\n",
"plt.plot(t_vals, a_vals, label=\"Acceleration $a(t)$\")\n",
"\n",
"plt.xlabel(\"t\")\n",
"plt.ylabel(\"Value\")\n",
"plt.ylim(0, 20)\n",
"plt.title(\"Position, Velocity, and Acceleration vs Time\")\n",
"plt.legend()\n",
"plt.grid(True)\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "a92b84a5",
"metadata": {},
"source": [
"#### 5. A wave height is given by $H(t) = \\sin(2t)$. Find the rate of change of height at $t = \\pi/6$."
]
},
{
"cell_type": "markdown",
"id": "bb0ab11f",
"metadata": {},
"source": [
"#### solution:\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "be3cbde1",
"metadata": {},
"source": [
"- Differentiate: $H'(t)=2\\cos(2t)$ (chain rule).\n",
"\n",
"- Plug in $t=\\pi/6$: $2t=\\pi/3$, $\\cos(\\pi/3)=1/2$."
]
},
{
"cell_type": "markdown",
"id": "ba2256c8",
"metadata": {},
"source": [
"#### ❗ Bonus Question: Mean Girls limit problem ❗\n",
"\n",
"Solve the question asked to Cady Heron at the end of Mean Girls:\n",
"\n",
"
\n",
"\n",
"Hint: L'hopital's rule:\n",
"\n",
"\n",
"\n",
"$$\n",
"\\lim_{x \\to a} \\frac{f(x)}{g(x)} = \\lim_{x \\to a} \\frac{f'(x)}{g'(x)}\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "faa8fbb5",
"metadata": {},
"source": [
"#### solution:"
]
},
{
"cell_type": "markdown",
"id": "d4e79351",
"metadata": {},
"source": [
"**LIMIT DOES NOT EXIST**"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "workshop-docs",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python",
"version": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}