diff options
| author | Sebastiano Tronto <sebastiano.tronto@gmail.com> | 2021-05-25 17:10:49 +0200 |
|---|---|---|
| committer | Sebastiano Tronto <sebastiano.tronto@gmail.com> | 2021-05-25 17:10:49 +0200 |
| commit | d6c61d988bfa4255baf9cdae42db59ebee38363f (patch) | |
| tree | 118ff3c2424e735149c145524965a4a337e50beb /src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb | |
| parent | 46eef66b1e1571c77dc828d7e950b129b4c8bfd0 (diff) | |
| download | mathsoftware-d6c61d988bfa4255baf9cdae42db59ebee38363f.tar.gz mathsoftware-d6c61d988bfa4255baf9cdae42db59ebee38363f.zip | |
Added files
Diffstat (limited to 'src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb')
| -rw-r--r-- | src/Homework4/.ipynb_checkpoints/Homework4-solutions-checkpoint.ipynb | 61 |
1 files changed, 61 insertions, 0 deletions
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 @@ | |||
| 1 | { | ||
| 2 | "cells": [ | ||
| 3 | { | ||
| 4 | "cell_type": "code", | ||
| 5 | "execution_count": 40, | ||
| 6 | "metadata": {}, | ||
| 7 | "outputs": [ | ||
| 8 | { | ||
| 9 | "name": "stdout", | ||
| 10 | "output_type": "stream", | ||
| 11 | "text": [ | ||
| 12 | "f(x) \t Derivative \t Integral \t Series expansion\n", | ||
| 13 | "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", | ||
| 14 | "sin(x) \t cos(x) \t -cos(x) \t 1*x + (-1/6)*x^3 + Order(x^5)\n", | ||
| 15 | "cos(x) \t -sin(x) \t sin(x) \t 1 + (-1/2)*x^2 + 1/24*x^4 + Order(x^5)\n", | ||
| 16 | "tan(x) \t tan(x)^2 + 1 \t log(sec(x)) \t 1*x + 1/3*x^3 + Order(x^5)\n", | ||
| 17 | "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", | ||
| 18 | "(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" | ||
| 19 | ] | ||
| 20 | } | ||
| 21 | ], | ||
| 22 | "source": [ | ||
| 23 | "print(\"f(x)\", \"\\t\", \"Derivative\", \"\\t\", \"Integral\", \"\\t\", \"Series expansion\")\n", | ||
| 24 | "var('a')\n", | ||
| 25 | "f(x) = (1+x)^a\n", | ||
| 26 | "assume(a>0)\n", | ||
| 27 | "functions = [e^x, sin, cos, tan, log(1+x), f]\n", | ||
| 28 | "for g in functions:\n", | ||
| 29 | " print(g(x), \"\\t\", derivative(g(x), x), \"\\t\", integral(g(x),x), \"\\t\", g(x).series(x==0,5))" | ||
| 30 | ] | ||
| 31 | }, | ||
| 32 | { | ||
| 33 | "cell_type": "code", | ||
| 34 | "execution_count": null, | ||
| 35 | "metadata": {}, | ||
| 36 | "outputs": [], | ||
| 37 | "source": [] | ||
| 38 | } | ||
| 39 | ], | ||
| 40 | "metadata": { | ||
| 41 | "kernelspec": { | ||
| 42 | "display_name": "SageMath 9.2", | ||
| 43 | "language": "sage", | ||
| 44 | "name": "sagemath" | ||
| 45 | }, | ||
| 46 | "language_info": { | ||
| 47 | "codemirror_mode": { | ||
| 48 | "name": "ipython", | ||
| 49 | "version": 3 | ||
| 50 | }, | ||
| 51 | "file_extension": ".py", | ||
| 52 | "mimetype": "text/x-python", | ||
| 53 | "name": "python", | ||
| 54 | "nbconvert_exporter": "python", | ||
| 55 | "pygments_lexer": "ipython3", | ||
| 56 | "version": "3.8.5" | ||
| 57 | } | ||
| 58 | }, | ||
| 59 | "nbformat": 4, | ||
| 60 | "nbformat_minor": 4 | ||
| 61 | } | ||
