From d6c61d988bfa4255baf9cdae42db59ebee38363f Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date: Tue, 25 May 2021 17:10:49 +0200
Subject: Added files

---
 .../Homework4-solutions-checkpoint.ipynb           | 61 ++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb

(limited to 'src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb')

diff --git a/src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb b/src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb
new file mode 100644
index 0000000..f8617fd
--- /dev/null
+++ b/src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb
@@ -0,0 +1,61 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f(x) \t Derivative \t Integral \t Series expansion\n",
+      "e^x \t e^x \t e^x \t 1 + 1*x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + Order(x^5)\n",
+      "sin(x) \t cos(x) \t -cos(x) \t 1*x + (-1/6)*x^3 + Order(x^5)\n",
+      "cos(x) \t -sin(x) \t sin(x) \t 1 + (-1/2)*x^2 + 1/24*x^4 + Order(x^5)\n",
+      "tan(x) \t tan(x)^2 + 1 \t log(sec(x)) \t 1*x + 1/3*x^3 + Order(x^5)\n",
+      "log(x + 1) \t 1/(x + 1) \t (x + 1)*log(x + 1) - x - 1 \t 1*x + (-1/2)*x^2 + 1/3*x^3 + (-1/4)*x^4 + Order(x^5)\n",
+      "(x + 1)^a \t a*(x + 1)^(a - 1) \t (x + 1)^(a + 1)/(a + 1) \t 1 + (a)*x + (1/2*a^2 - 1/2*a)*x^2 + (1/6*a^3 - 1/2*a^2 + 1/3*a)*x^3 + (1/24*a^4 - 1/4*a^3 + 11/24*a^2 - 1/4*a)*x^4 + Order(x^5)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"f(x)\", \"\\t\", \"Derivative\", \"\\t\", \"Integral\", \"\\t\", \"Series expansion\")\n",
+    "var('a')\n",
+    "f(x) = (1+x)^a\n",
+    "assume(a>0)\n",
+    "functions = [e^x, sin, cos, tan, log(1+x), f]\n",
+    "for g in functions:\n",
+    "    print(g(x), \"\\t\", derivative(g(x), x), \"\\t\", integral(g(x),x), \"\\t\", g(x).series(x==0,5))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.2",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
-- 
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