{ "cells": [ { "cell_type": "markdown", "id": "720ed4ef-df76-44b0-a812-794f336f31be", "metadata": {}, "source": [ "# Sample Lab" ] }, { "cell_type": "markdown", "id": "33f10de1-4028-4ede-9859-10c42e1b7060", "metadata": {}, "source": [ "**John Smith**" ] }, { "cell_type": "markdown", "id": "27a93b71-4fc8-4211-a08c-929424f89c5e", "metadata": {}, "source": [ "*Calculus I*" ] }, { "cell_type": "markdown", "id": "d49a358d-7935-470b-b346-166c4c872952", "metadata": {}, "source": [ "I have finished my reading assignment on [derivatives](https://en.wikipedia.org/wiki/Derivative). In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances." ] }, { "cell_type": "code", "execution_count": 1, "id": "8e665357-a711-4a59-9197-a663e19b2cf9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
tnpham@eou.edu
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" ], "text/plain": [ " 2\n", "(-1 + x) (-1 + x + x )" ] }, "execution_count": 4, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Factor[x^3-2x+1]" ] }, { "cell_type": "code", "execution_count": 5, "id": "c33a213c-79f5-4f13-981e-5181be9718af", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ " 2 3 4 5 6 7 8\n", "1 + 20 x + 180 x + 960 x + 3360 x + 8064 x + 13440 x + 15360 x + 11520 x + \n", " \n", " 9 10\n", "> 5120 x + 1024 x" ] }, "execution_count": 5, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Expand[(1+2x)^10]" ] }, { "cell_type": "code", "execution_count": 6, "id": "0c84fbed-edf6-487b-bd3b-73136417ecd8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ " Sin[x]\n", "E Cos[x]" ] }, "execution_count": 6, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "D[E^(Sin[x]),x]" ] }, { "cell_type": "code", "execution_count": 7, "id": "feb4ed33-9fe6-4239-98f1-0f235425a60a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ " 2 3 4 5 6 7 8\n", "1 + 20 x + 180 x + 960 x + 3360 x + 8064 x + 13440 x + 15360 x + 11520 x + \n", " \n", " 9 10\n", "> 5120 x + 1024 x" ] }, "execution_count": 7, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Expand[(1+2x)^10]" ] }, { "cell_type": "code", "execution_count": 8, "id": "8e288244-3eff-40da-bf3a-6fac82ffef72", "metadata": {}, "outputs": [], "source": [ "CopyToClipboard[%]" ] }, { "cell_type": "code", "execution_count": 9, "id": "7bd34239-64b2-4859-b418-04aead5e05d6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ " 2 3 4 5 6 7 8\n", "1 + 20 x + 180 x + 960 x + 3360 x + 8064 x + 13440 x + 15360 x + 11520 x + \n", " \n", " 9 10\n", "> 5120 x + 1024 x" ] }, "execution_count": 9, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "1 + 20 x + 180 x^2 + 960 x^3 + 3360 x^4 + 8064 x^5 + 13440 x^6 + \n", " 15360 x^7 + 11520 x^8 + 5120 x^9 + 1024 x^10" ] }, { "cell_type": "code", "execution_count": 10, "id": "cb0002d2-ee2a-4434-b912-df7837c779c2", "metadata": {}, "outputs": [], "source": [ "CopyToClipboard[Expand[(1+2x)^10]]" ] }, { "cell_type": "code", "execution_count": 11, "id": "3fc23e71-02aa-4e2c-bdd0-fa9bf5bf8773", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ " 2 3 4 5 6 7 8\n", "1 + 20 x + 180 x + 960 x + 3360 x + 8064 x + 13440 x + 15360 x + 11520 x + \n", " \n", " 9 10\n", "> 5120 x + 1024 x" ] }, "execution_count": 11, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "1 + 20 x + 180 x^2 + 960 x^3 + 3360 x^4 + 8064 x^5 + 13440 x^6 + \n", " 15360 x^7 + 11520 x^8 + 5120 x^9 + 1024 x^10" ] }, { "cell_type": "markdown", "id": "1edcb9ce-a5d7-4796-bbcd-a8aaa8bde648", "metadata": {}, "source": [ "Below is the graph of the function $f(x)=\\frac{\\sin x}{\\sin^2(2x)}$ on the interval $[0,10]$." ] }, { "cell_type": "code", "execution_count": 12, "id": "08e8ad31-6afd-49b7-9e3d-11d713f4136b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ "-Graphics-" ] }, "execution_count": 12, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Plot[Sin[x]/Sin[2x]^2,{x,0,10}]" ] }, { "cell_type": "code", "execution_count": 13, "id": "e4393eb6-ef9e-422e-b533-7acd4f0e9be2", "metadata": {}, "outputs": [], "source": [ "CopyToClipboard[%]" ] }, { "cell_type": "code", "execution_count": 14, "id": "9cf6e4c6-fe07-4f26-a3fe-53402d2d72d2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ "Legended[-Graphics-, Placed[LineLegend[{Directive[Opacity[1.], \n", " \n", "> RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6]], \n", " \n", "> Directive[Opacity[1.], RGBColor[0.880722, 0.611041, 0.142051], \n", " \n", "> AbsoluteThickness[1.6]], Directive[Opacity[1.], \n", " \n", "> RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6]]}, \n", " \n", "> {Sin[x], Sin[2 x], Sin[3 x]}, LegendMarkers -> None, LabelStyle -> {}, \n", " \n", "> LegendLayout -> Column], After, Identity]]" ] }, "execution_count": 14, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,Pi},PlotLegends->\"Expressions\"]" ] }, { "cell_type": "code", "execution_count": 16, "id": "ce8f8c9d-534b-4b5c-8dd0-8d46064f3dce", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [] }, "execution_count": 16, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Interact@Plot3D[x^2-y^2,{x,-4,4},{y,-4,4}]" ] }, { "cell_type": "code", "execution_count": 18, "id": "0db0dc5d-5747-42c0-901d-af31a092b02b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [] }, "execution_count": 18, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Interact@ParametricPlot3D[{t*Cos[t],t*Sin[t],t},{t,0,30}]" ] }, { "cell_type": "code", "execution_count": 9, "id": "311c1f2f-d894-41d3-bb87-8ce4ca865653", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [] }, "execution_count": 9, "metadata": { "text/html": [], "text/plain": [] }, "output_type": "execute_result" } ], "source": [ "Interact@Manipulate[ParametricPlot3D[{t*Cos[t],t*Sin[t],t},{t,0,s}, \n", "PlotRange->{{-30,30},{-30,30},{0,30}}], {s,0.1,30}]" ] }, { "cell_type": "code", "execution_count": null, "id": "5ba974d4-6b10-44ed-b468-3ab5180748d1", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Wolfram Language 13.1", "language": "Wolfram Language", "name": "wolframlanguage13.1" }, "language_info": { "codemirror_mode": "mathematica", "file_extension": ".m", "mimetype": "application/vnd.wolfram.m", "name": "Wolfram Language", "pygments_lexer": "mathematica", "version": "12.0" } }, "nbformat": 4, "nbformat_minor": 5 }