{ "cells": [ { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Name: Nathan Nguyen\n", "# I worked on this code with: Eri, Mika, Cindy\n", "\n", "# Please do all of your work for this week's lab in this worksheet. If\n", "# you wish to create other worksheets for scratch work, you can, but\n", "# this is the one that will be graded. You do not need to do anything\n", "# to turn in your lab. It will be collected by your TA at the beginning\n", "# of (or right before) next week’s lab.\n", "\n", "# Be sure to clearly label which question you are answering as you go and to\n", "# use enough comments that you and the grader can understand your code.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": "\n\n", "text/plain": [ "Graphics3d Object" ] }, "execution_count": 9, "metadata": { }, "output_type": "execute_result" } ], "source": [ "#1\n", "var(\"X,Y\")\n", "func1 = (X^2)+(Y^2)+(3*X)+(5*Y)\n", "plot3d(func1, (X,-5,5),(Y,-5,5))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" } ], "source": [ "#2\n", "func2 = X^2+3*X\n", "der2 = diff(func2,X)\n", "der2a = der2(0) #slope at x = 0\n", "plot(func2)+plot(0+der2a*(X),color=\"red\", axes_labels = [\"X\",\"Z\"])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 11, "metadata": { }, "output_type": "execute_result" } ], "source": [ "#3\n", "func3 = Y^2+5*Y\n", "der3 = diff(func3,Y)\n", "der3a = der3(0) #slope at y = 0\n", "plot(func3)+plot(der3(0)*X,color=\"red\", axes_labels = [\"Y\",\"Z\"])" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": "\n\n", "text/plain": [ "Graphics3d Object" ] }, "execution_count": 12, "metadata": { }, "output_type": "execute_result" } ], "source": [ "#4\n", "var(\"X,Y\")\n", "plot3d(der2a*X+der3a*Y,(X,-5,5),(Y,-5,5), color = \"red\", opacity = 0.5) + plot3d(func1, (X,-5,5),(Y,-5,5))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": "\n\n", "text/plain": [ "Graphics3d Object" ] }, "execution_count": 13, "metadata": { }, "output_type": "execute_result" } ], "source": [ "#5\n", "z5 = 2*(X-2)-1*(Y-3)+7\n", "plot3d(z5,(X,-10,10),(Y,-10,10)) + point3d((2,3,7), size = 100, color = \"red\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": "\n