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+ {
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+ "cells": [
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+ {
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+ "cell_type": "raw",
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+ "id": "8c69730d",
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+ "metadata": {},
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+ "source": [
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+ "---\n",
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+ "title: Calculus Problem Generator\n",
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+ "description: Generates Derivative and Integral Expressions at https://nsc9.github.io/\n",
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+ "show-code : False\n",
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+ "---"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 1,
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+ "id": "c5197005",
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+ "metadata": {},
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+ "outputs": [],
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+ "source": [
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+ "# recent change: Added useful links, Added plaintext version of expressions for easy copy/paste to a solver."
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+ ]
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+ },
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+ {
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+ "cell_type": "markdown",
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+ "id": "6bdf2faf",
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+ "metadata": {},
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+ "source": [
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+ "# Solve with pen and paper:"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 2,
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+ "id": "108761f9",
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+ "metadata": {
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+ "scrolled": false
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+ },
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+ "outputs": [],
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+ "source": [
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+ "from sympy.simplify.fu import TR22,TR2i\n",
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+ "from sympy import ln,exp,Function,Derivative,Eq,Integral,factor_terms, sqrt, Symbol,Limit\n",
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+ "from sympy import sin,cos,tan,Rational,nsimplify\n",
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+ "import random\n",
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+ "f = Function('f')\n",
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+ "g = Function('g')\n",
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+ "h = Function('h')\n",
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+ "theta = Symbol('theta')\n",
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+ "i = 0\n",
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+ "dkeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\",\"li\",\"erf\",\"Si\",\"Ci\",\"hyper\",\"fresnel\",\"Li\",\"expint\",\"zoo\",\n",
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+ "\"nan\",\"oo\",\"abs\",\"re\",\"EulerGamma\", \"sinh\",\"tanh\", \"cosh\",'sign','abs','atan','csc','asin'} \n",
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+ "ikeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\", \"li\", \"erf\", \"atan\", \"Si\", \"Ci\", \"hyper\", \"fresnel\", \"Li\", \n",
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+ "\"expint\",\"zoo\", \"nan\", \"oo\",\"EulerGamma\",\"sinh\",\"csc\",\"asin\"}\n",
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+ "keywords2 = {\"sin\",\"cos\",\"tan\"}\n",
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+ "def random_variable(i):\n",
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+ " return Symbol(random.choice([i for i in ['v','t','x','z','y']]), real=True)\n",
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+ "def random_value(i):\n",
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+ " return random.choice([i for i in range(-10,10) if i not in [0]])\n",
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+ "def power(a): \n",
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+ " return random_value(i)*a**int(random_value(i)/2)\n",
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+ "def scalar(a): \n",
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+ " return a*random_value(i) + random_value(i)\n",
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+ "def addSUBTR(a): \n",
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+ " return a+random_value(i)\n",
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+ "def dmain(a):\n",
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+ " def random_math(a): \n",
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+ " funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt] \n",
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+ " operations = [f(a)*g(a)+h(a), f(a)-g(a)*h(a),f(a)/(g(a)-h(a)), f(a)/(-g(a)+h(a)),\n",
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+ " f(a)+g(a)+h(a), f(a)-g(a)-h(a),f(a)+g(a)-h(a), f(a)-g(a)+h(a),\n",
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+ " (f(a)*g(a))/h(a), f(a)/(g(a)*h(a)),f(g(h(a))),f(h(a))+g(a),f(h(a))-g(a),\n",
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+ " f(h(a))/g(a),f(a)/g(h(a)),f(h(a))*g(a),f(a)*h(a)*g(a)]\n",
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+ " operation = operations[random.randrange(0,len(operations))]\n",
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+ " return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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+ " [random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
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+ " return random_math(a)\n",
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+ "def imain(a):\n",
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+ " def random_math2(a): \n",
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+ " funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt] \n",
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+ " operations = [f(g(a)),f(a)+g(a),f(a)-g(a),f(a)/g(a),f(a)*g(a),\n",
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+ " f(g(a))**2,2*f(a)+g(a),2*f(a)-g(a),2*f(a)/g(a),2*f(a)*g(a)]\n",
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+ " operation = operations[random.randrange(0,len(operations))]\n",
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+ " return [[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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+ " [random.randrange(0,len(funs))]\n",
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+ " return random_math2(a)"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 8,
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+ "id": "5ddcf6a5",
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+ "metadata": {
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+ "scrolled": false
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+ },
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+ "outputs": [
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+ {
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+ "data": {
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+ "text/latex": [
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+ "$\\displaystyle a' = \\frac{d}{d \\theta} \\left(- 3 \\theta + \\tan{\\left(\\theta \\right)} - 14\\right)$"
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+ ],
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+ "text/plain": [
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+ "Eq(a', Derivative(-3*theta + tan(theta) - 14, theta))"
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+ ]
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+ },
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+ "metadata": {},
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+ "output_type": "display_data"
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+ },
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+ {
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+ "data": {
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+ "text/latex": [
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+ "$\\displaystyle B = \\int 3 \\log{\\left(x \\right)}\\, dx$"
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+ ],
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+ "text/plain": [
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+ "Eq(B, Integral(3*log(x), x))"
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+ ]
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+ },
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+ "metadata": {},
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+ "output_type": "display_data"
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+ }
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+ ],
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+ "source": [
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+ "derror = True\n",
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+ "def dtest():\n",
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+ " global setup1\n",
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+ " global derror\n",
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+ " global practice1\n",
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+ " a = random_variable(i)\n",
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+ " setup1 = dmain(a)\n",
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+ " practice1 = Derivative(setup1,a) \n",
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+ " p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
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+ " if any(kw in str(setup1) for kw in keywords2):\n",
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+ " setup1 = setup1.replace(a,theta)\n",
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+ " practice1 = Derivative(setup1,theta) \n",
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+ " p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
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+ " if p1eq.rhs != 0 and not any(kw in str(p1eq) for kw in dkeywords):\n",
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+ " derror = False\n",
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+ " return p1eq\n",
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+ "while derror == True: \n",
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+ " output1 = dtest()\n",
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+ "ierror = True\n",
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+ "def itest():\n",
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+ " global ierror\n",
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+ " global practice2\n",
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+ " global setup2\n",
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+ " a = random_variable(i)\n",
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+ " setup2 = imain(a)\n",
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+ " practice2 = Integral(setup2,a) \n",
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+ " p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
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+ " if str(factor_terms(p2eq.lhs)) != str(factor_terms(p2eq.rhs)) and not any(kw in str(p2eq) for kw in ikeywords)\\\n",
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+ " and str(p2eq.lhs) != str(-p2eq.rhs): \n",
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+ " if any(kw in str(setup2) for kw in keywords2):\n",
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+ " setup2 = setup2.replace(a,theta)\n",
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+ " practice2 = Integral(setup2,theta) \n",
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+ " p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
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+ " ierror = False\n",
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+ " return p2eq\n",
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+ "while ierror == True:\n",
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+ " output2 = itest()\n",
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+ "a1 = Symbol(\"a'\")\n",
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+ "B = Symbol('B')\n",
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+ "eq1 = Eq(a1,nsimplify(output1.lhs))\n",
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+ "eq2 = Eq(B,nsimplify(output2.lhs))\n",
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+ "eq3 = Eq(a1,nsimplify(output1.rhs))\n",
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+ "eq4 = Eq(B,nsimplify(output2.rhs))\n",
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+ "def lhs():\n",
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+ " display(eq1,eq2) \n",
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+ " return\n",
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+ "def rhs():\n",
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+ " return display(eq3,eq4)\n",
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+ "lhs()"
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+ ]
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+ },
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+ {
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+ "cell_type": "markdown",
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+ "id": "2393180e",
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+ "metadata": {},
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+ "source": [
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+ "___________________________________________________________________________________________________________________\n",
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+ "If LaTeX display breaks, refresh the page. Runtime is under a second if you run the Jupyter-Notebook locally.\n",
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+ "\n",
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+ "**Created by GitHub.com/NSC9 - https://nsc9.github.io/ - MIT License - v7.5**\n",
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+ "\n",
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+ "Latest version source code: https://github.com/NSC9/Sample_of_Work/tree/Main/Artificial_Calculus_Teacher\n",
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+ "\n",
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+ "Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**\n",
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+ "\n"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 9,
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+ "id": "15c3f34f",
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "name": "stdout",
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+ "output_type": "stream",
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+ "text": [
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+ "Derivative(-3*theta + tan(theta) - 14, theta)\n",
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+ "Integral(3*log(x), x)\n"
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+ ]
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+ }
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+ ],
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+ "source": [
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+ "print(eq1.rhs)\n",
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+ "print(eq2.rhs)"
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+ ]
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+ },
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+ {
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+ "cell_type": "markdown",
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+ "id": "30b55c90",
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+ "metadata": {},
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+ "source": [
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+ "https://www.derivative-calculator.net/\n",
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+ "\n",
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+ "https://www.integral-calculator.com/\n",
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+ "___________________________________________________________________________________________________________________\n",
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+ "\n",
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+ "# Answers:"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 10,
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+ "id": "fbec286d",
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "data": {
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+ "text/latex": [
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+ "$\\displaystyle a' = \\sec^{2}{\\left(\\theta \\right)} - 3$"
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+ ],
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+ "text/plain": [
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+ "Eq(a', sec(theta)**2 - 3)"
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+ ]
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+ },
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+ "metadata": {},
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+ "output_type": "display_data"
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+ },
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+ {
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+ "data": {
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+ "text/latex": [
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+ "$\\displaystyle B = 3 x \\log{\\left(x \\right)} - 3 x$"
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+ ],
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+ "text/plain": [
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+ "Eq(B, 3*x*log(x) - 3*x)"
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+ ]
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+ },
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+ "metadata": {},
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+ "output_type": "display_data"
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+ }
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+ ],
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+ "source": [
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+ "rhs()"
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+ ]
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+ }
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+ ],
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+ "metadata": {
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+ "kernelspec": {
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+ "display_name": "Python 3 (ipykernel)",
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+ "language": "python",
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+ "name": "python3"
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+ },
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+ "language_info": {
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+ "codemirror_mode": {
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+ "name": "ipython",
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+ "version": 3
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+ },
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+ "file_extension": ".py",
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+ "mimetype": "text/x-python",
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+ "name": "python",
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+ "nbconvert_exporter": "python",
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+ "pygments_lexer": "ipython3",
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+ "version": "3.8.10"
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+ }
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+ },
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+ "nbformat": 4,
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+ "nbformat_minor": 5
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+ }