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248 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 249 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 250 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 206 "" 0 "" {TEXT 206 28 "Lab 1: Introduction to Maple" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{EXCHG {PARA 15 "" 0 "" {TEXT 252 14 "The following " }{TEXT 209 7 "restart" }{TEXT 252 62 " command clears Maple's memory. Place \+ the cursor next to the " }{TEXT 210 7 "restart" }{TEXT 252 25 " comman d and press Enter." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{EXCHG {PARA 0 "> " 0 "restart" {MPLTEXT 1 0 8 "restart;" }{TEXT 251 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 125 " Each square with a plus in it is called a \"section.\" Click on these squares to expand the section and get more information. " }}{PARA 0 " " 0 "" {TEXT 251 122 "Make sure that you execute every Maple command ( in red) by putting your cursor next to it and pressing the ENTER butto n. " }}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 5 "Goals" }}{PARA 0 "" 0 "" {TEXT 251 122 "Students will use the appropriate Maple commands to per form the numerical, algebraic, and graphical exercises given below." } }}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 10 "Discussion" }}{PARA 0 "" 0 "" {TEXT 251 76 "For every lab in this manual, we provide examples of the Maple commands (in " }{TEXT 211 4 "bold" }{TEXT 251 216 " print) that you will need to complete the questions that follow. Read through th e following worksheet carefully, taking notes on the commands that are demonstrated so that you can complete the activity at the end. " }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 253 11 "Input Modes" }}{PARA 0 "" 0 "" {TEXT 251 123 "Maple has two main input modes: command and text. In o rder to execute a calculation, Maple must be in command mode. The " }{TEXT 212 2 "[>" }{TEXT 251 126 " symbol next to the cursor on your \+ screen indicates that maple is in command mode. To put Maple in comma nd mode, click the " }{TEXT 213 2 "[>" }{TEXT 251 64 " button on the tool bar and then type your command next to the " }{TEXT 214 2 "[>" } {TEXT 251 39 " symbol that appears on your screen. " }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 158 "In order to write a n explanation to a lab question, Maple must be in text mode (so that i t acts like a word processor). To put Maple in text mode, click the " }{TEXT 215 1 "T" }{TEXT 251 25 " button on the tool bar. " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 22 "Numerical Calculations" }}{PARA 0 "" 0 "" {TEXT 251 225 "At its most basic level, Maple is a very powerful ca lculator. You can use the following arithmetic operations: +, -, *, \+ /, ^ which are addition, subtraction, multiplication, division, and \+ raising to a power, respectively." }}{PARA 0 "" 0 "" {TEXT 251 18 "To \+ calculate (32)(" }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\" \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Ty pesetting:-msup(Typesetting:-mn(\"12\", mathvariant = \"normal\"), Typ esetting:-mn(\"13\", mathvariant = \"normal\"), superscriptshift = \"0 \")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF $6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6#-I%msupGF$6%-I# mnGF$6$Q#12F'/F3Q'normalF'-F;6$Q#13F'F>/%1superscriptshiftGQ\"0F'F+" } {TEXT 251 32 ") you would enter the following:" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "32*12^13;" } }}{PARA 0 "" 0 "" {TEXT 251 61 "Place your cursor on the above command line and press ENTER. " }{TEXT 216 115 "Note that each command is fol lowed by a semicolon. Also observe that you must use \"*\" to tell Ma ple to multiply. " }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 178 "Maple uses the standard order of operations. To be su re that operations are performed in the desired order, use parentheses . Press enter after each of the next two commands. " }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(2+4)/7; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2+4/7;" }}}{PARA 0 "" 0 "" {TEXT 251 121 "Be sure to use round parentheses rather than square \+ brackets [ ] or curly braces \{ \}, which have other meanings in Maple ." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 42 "To calculate (2+3)(3-1), enter the command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(2+3)*(3-1);" }}}{PARA 0 "" 0 "" {TEXT 251 54 "Note t hat the multiplication operator * is required. " }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 193 "Maple recognizes a wid e variety of special operators including factorial, greatest common di visor, and least common multiple. The following line is an example of the factorial operator in use." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "200!; " }}}{PARA 0 "" 0 "" {TEXT 251 102 "Your cursor should al ready be in place in the above command line. Press ENTER to see the ex pansion of " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", i talic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typeset ting:-mn(\"200\", mathvariant = \"normal\"), Typesetting:-mo(\"!\", ma thvariant = \"normal\", fence = \"false\", separator = \"false\", stre tchy = \"false\", symmetric = \"false\", largeop = \"false\", movablel imits = \"false\", accent = \"false\", lspace = \"0.1111111em\", rspac e = \"0.1111111em\")), Typesetting:-mi(\"\", italic = \"true\", mathva riant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sy slibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6 $-I#mnGF$6$Q$200F'/F3Q'normalF'-I#moGF$6-Q\"!F'F;/%&fenceGQ&falseF'/%* separatorGFC/%)stretchyGFC/%*symmetricGFC/%(largeopGFC/%.movablelimits GFC/%'accentGFC/%'lspaceGQ,0.1111111emF'/%'rspaceGFRF+" }{TEXT 251 1 " ." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 49 "Yo u can easily include the previous expansion of " }{XPPEDIT 18 0 "Types etting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \" italic\"), Typesetting:-mrow(Typesetting:-mn(\"200\", mathvariant = \" normal\"), Typesetting:-mo(\"!\", mathvariant = \"normal\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.1111111em\", rspace = \"0.1111111em\")), Typesetting :-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6# /I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ %trueF'/%,mathvariantGQ'italicF'-F#6$-I#mnGF$6$Q$200F'/F3Q'normalF'-I# moGF$6-Q\"!F'F;/%&fenceGQ&falseF'/%*separatorGFC/%)stretchyGFC/%*symme tricGFC/%(largeopGFC/%.movablelimitsGFC/%'accentGFC/%'lspaceGQ,0.11111 11emF'/%'rspaceGFRF+" }{TEXT 251 112 " in any subsequent calculation w ithout having to type it. The ditto operator, represented by a percent age sign, " }{TEXT 217 1 "%" }{TEXT 251 139 ", refers to the last exp ression computed by Maple. (For more information on the ditto operator , see the help page for ditto.) The command " }{TEXT 218 7 "ifactor" } {TEXT 251 54 " factors the previous result into its prime factors. " }}{EXCHG {PARA 0 "> " 0 "ifactor" {MPLTEXT 1 0 11 "ifactor(%);" }}} {PARA 0 "" 0 "" {TEXT 251 30 "Press ENTER to see the result." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 86 "The next comm and calculates the product again, which is precisely the value of 200! . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}}{PARA 0 "" 0 "" {TEXT 251 30 "Press ENTER to see the result." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 346 "A principal streng th of Maple is its ability to do exact arithmetic. Fractions and radic als during computation are not immediately converted to their decimal \+ equivalent, thereby avoiding round-off errors. When you need to use de cimal equivalents, Maple has a command that approximates the value of \+ the expression in a decimal floating-point form." }}{PARA 0 "" 0 "" {TEXT 251 24 "Consider the expression " }{XPPEDIT 18 0 "Typesetting:-m row(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting :-mn(\"2\", mathvariant = \"normal\"), Typesetting:-mn(\"30\", mathvar iant = \"normal\"), superscriptshift = \"0\"), Typesetting:-mo(\"&Invi sibleTimes;\", mathvariant = \"normal\", fence = \"false\", separator \+ = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0 em\", rspace = \"0.0em\"), Typesetting:-msqrt(Typesetting:-mn(\"3\", m athvariant = \"normal\"))), Typesetting:-mrow(Typesetting:-mi(\"\", it alic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typesett ing:-msup(Typesetting:-mn(\"3\", mathvariant = \"normal\"), Typesettin g:-mn(\"20\", mathvariant = \"normal\"), superscriptshift = \"0\")), T ypesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), li nethickness = \"1\", denomalign = \"center\", numalign = \"center\", b evelled = \"false\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_s yslibGF'6#-I&mfracGF$6(-F#6%-I%msupGF$6%-I#mnGF$6$Q\"2F'/%,mathvariant GQ'normalF'-F46$Q#30F'F7/%1superscriptshiftGQ\"0F'-I#moGF$6-Q1&Invisib leTimes;F'F7/%&fenceGQ&falseF'/%*separatorGFF/%)stretchyGFF/%*symmetri cGFF/%(largeopGFF/%.movablelimitsGFF/%'accentGFF/%'lspaceGQ&0.0emF'/%' rspaceGFU-I&msqrtGF$6#-F46$Q\"3F'F7-F#6%-I#miGF$6%Q!F'/%'italicGQ%true F'/F8Q'italicF'-F#6#-F16%Fen-F46$Q#20F'F7F=Fjn/%.linethicknessGQ\"1F'/ %+denomalignGQ'centerF'/%)numalignGF_p/%)bevelledGFF" }{TEXT 251 57 " \+ , which is entered on the Maple command line as follows." }}{EXCHG {PARA 0 "> " 0 "sqrt" {MPLTEXT 1 0 20 "(2^30/3^20)*sqrt(3);" }}}{PARA 0 "" 0 "" {TEXT 251 49 "Press ENTER to see the results of this express ion" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 10 " Using the " }{TEXT 219 5 "evalf" }{TEXT 251 90 " command, you can gene rate an approximation in the form of a decimal floating-point value." }}{EXCHG {PARA 0 "> " 0 "evalf" {MPLTEXT 1 0 9 "evalf(%);" }}}{PARA 0 "" 0 "" {TEXT 251 52 "Press ENTER to see the decimal floating-point va lue." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 4 "Help" }}{PARA 0 "" 0 "" {TEXT 251 71 "If you eve r need additional information about a Maple command, ask for " }{TEXT 220 4 "Help" }{TEXT 251 75 " by typing in a question mark followed by \+ the Maple command and then press " }{TEXT 221 5 "Enter" }{TEXT 251 27 ". For example, type in " }{TEXT 222 3 "?+ " }{TEXT 251 16 " and t hen press " }{TEXT 223 5 "Enter" }{TEXT 251 116 ". A help window will open that gives information on the various arithmetic operations that are available in Maple ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 " ?+" }}}{PARA 0 "" 0 "" {TEXT 251 25 "You can also open up the " }{TEXT 224 5 "Help " }{TEXT 251 261 "menu by clicking on the \"Help\" option on your tool bar. When you click on \"Help\", a menu scrolls down wi th many options. The \"introduction\" will give you a grid of topics, and the \"topic search\" allows you to type in certain word items tha t you may need. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT 251 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 19 "Assigning Variables" }}{PARA 0 "" 0 "" {TEXT 206 59 "Names or labe ls can be used to store and refer to results. " }{TEXT 251 1 " " } {TEXT 225 54 "Assignment statements use the colon-equal symbol \":=''" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A := 5;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}}{PARA 0 "" 0 "" {TEXT 251 68 "This means tha t the variable \"A'' has been assigned the value 5 and " }{TEXT 226 25 "it will retain this value" }{TEXT 251 91 " through the remainder o f the session unless you assign it another value or \"unassign\" it." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "4*A+12;" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 63 "The following statement is the way to \"unassign\" the \+ variable." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "A := 'A';" }}} {PARA 0 "" 0 "" {TEXT 251 78 "Note that in the last statement we have \+ enclosed A within two single quotes '." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 44 "Maple Constants and Maple Built-in Functions" } }{PARA 0 "" 0 "" {TEXT 251 192 "Maple has many of the the standard mat hematical constants built-in. Maple is also \"case sensitive\" , whi ch means that it treats \"a\" and \"A\" as distinct symbols. The math ematical constants " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-m i(\"π\", italic = \"false\", mathvariant = \"normal\"));" "-I%mrowG 6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q%πF'/%'it alicGQ&falseF'/%,mathvariantGQ'normalF'" }{TEXT 251 69 " (the ratio o f the circumference of a circle to its diameter), and " }{TEXT 227 1 "i" }{TEXT 251 38 " (the pure imaginary number such that " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathv ariant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting: -mi(\"i\", italic = \"true\", mathvariant = \"italic\"), Typesetting:- mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Types etting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%m rowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'it alicGQ%trueF'/%,mathvariantGQ'italicF'-F#6#-I%msupGF$6%-F,6%Q\"iF'F/F2 -I#mnGF$6$Q\"2F'/F3Q'normalF'/%1superscriptshiftGQ\"0F'F+" }{TEXT 251 50 "= -1) are denoted by \"Pi\", and \"I\" respectively." }}{EXCHG {PARA 0 "> " 0 "Pi" {MPLTEXT 1 0 3 "Pi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(%%,50);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "I^2;" }{TEXT 251 0 "" }}}{PARA 0 " " 0 "" {TEXT 251 71 "Maple also has many built in functions. Your tri gonometric functions, " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting: -msup(Typesetting:-mi(\"e\", italic = \"true\", mathvariant = \"italic \"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic \"), superscriptshift = \"0\"));" "-I%mrowG6#/I+modulenameG6\"I,Typese ttingGI(_syslibGF'6#-I%msupGF$6%-I#miGF$6%Q\"eF'/%'italicGQ%trueF'/%,m athvariantGQ'italicF'-F/6%Q\"xF'F2F5/%1superscriptshiftGQ\"0F'" }{TEXT 251 157 ", square root, etc. are all functions that Maple has built i n to its system. Let's calculate the sine, cosine, tangent, cosecant, secant, and cotangent of " }{XPPEDIT 18 0 "Typesetting:-mrow(Typeset ting:-mi(\"π\", italic = \"false\", mathvariant = \"normal\"));" "- I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q%π F'/%'italicGQ&falseF'/%,mathvariantGQ'normalF'" }{TEXT 251 1 "." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sin(Pi);cos(Pi);tan(Pi);csc( Pi);sec(Pi);cot(Pi);" }}}{PARA 0 "" 0 "" {TEXT 251 281 "Note the follo wing items: (1) The trigonometric functions use the same notation that you use. (2) The argument for the trigonometric function has to be i n parentheses. (3) Maple calls divison by zero a singularity. (4) Yo u can enter several execution statements into one line. " }}{PARA 0 " " 0 "" {TEXT 251 19 "Now let's evaluate " }{XPPEDIT 18 0 "Typesetting: -mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"e\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", mathvar iant = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\"\", \+ italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulena meG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,m athvariantGQ'italicF'-F#6#-I%msupGF$6%-F,6%Q\"eF'F/F2-I#mnGF$6$Q\"2F'/ F3Q'normalF'/%1superscriptshiftGQ\"0F'F+" }{TEXT 251 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(2);" }{TEXT 251 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 31 "Note that the M aple command is " }{TEXT 228 3 "exp" }{TEXT 251 81 " and that the powe r has to be in parentheses. To get a decimal approximation of " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typ esetting:-mi(\"e\", italic = \"true\", mathvariant = \"italic\"), Type setting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\" )), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\") );" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6% Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6#-I%msupGF$6%-F,6%Q \"eF'F/F2-I#mnGF$6$Q\"2F'/F3Q'normalF'/%1superscriptshiftGQ\"0F'F+" } {TEXT 251 10 ", use the " }{TEXT 229 5 "evalf" }{TEXT 251 9 " command: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 51 "As for the square \+ root of 2, you type as follows. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(2);" }{TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }{TEXT 251 0 "" }} {PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}} {PARA 0 "" 0 "" {TEXT 251 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 24 " Algebraic computations" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 254 35 "Exp anding and Factoring Expressions" }}{PARA 0 "" 0 "" {TEXT 251 36 "Mapl e can expand binomials such as " }{XPPEDIT 18 0 "Typesetting:-mrow(Ty pesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Type setting:-mrow(Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow (Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), \+ Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi(\"y\", \+ italic = \"true\", mathvariant = \"italic\")), mathvariant = \"normal \"), Typesetting:-mn(\"15\", mathvariant = \"normal\"), superscriptshi ft = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+ \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 %-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6#-I%msup GF$6%-I(mfencedGF$6$-F#6%-F,6%Q\"xF'F/F2-I#moGF$6-Q\"+F'/F3Q'normalF'/ %&fenceGQ&falseF'/%*separatorGFJ/%)stretchyGFJ/%*symmetricGFJ/%(largeo pGFJ/%.movablelimitsGFJ/%'accentGFJ/%'lspaceGQ,0.2222222emF'/%'rspaceG FY-F,6%Q\"yF'F/F2FF-I#mnGF$6$Q#15F'FF/%1superscriptshiftGQ\"0F'F+" } {TEXT 251 73 ". The following Maple commands create the expression, an d then expand it." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expr := (x+y)^15;" }}}{EXCHG {PARA 0 "> " 0 "expand" {MPLTEXT 1 0 13 "expand( expr);" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 65 "Note that in the above example, we first defined the expression, " }{TEXT 230 7 "expr. " }{TEXT 251 28 "We can also expand directly." } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand((x+y)^15);" }}} {PARA 0 "" 0 "" {TEXT 251 67 "Press ENTER three times to see the resul ts of these Maple commands." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 42 "After viewing the result, you can use the " } {TEXT 231 6 "factor" }{TEXT 251 56 " command to factor it in order to \+ check the computation." }}{EXCHG {PARA 0 "> " 0 "factor" {MPLTEXT 1 0 10 "factor(%);" }}}{PARA 0 "" 0 "" {TEXT 251 63 "Press [Enter] to fact or the results of the previous expression." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 254 23 "Simplifying Expressions" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 113 "Maple can apply identi ties to simplify many lengthy mathematical expressions, such as trigon ometric expressions. " }}{PARA 0 "" 0 "" {TEXT 251 9 "Consider " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Types etting:-msup(Typesetting:-mrow(Typesetting:-mi(\"cos\", italic = \"fal se\", mathvariant = \"normal\"), Typesetting:-mo(\"⁡\", \+ mathvariant = \"normal\", fence = \"false\", separator = \"false\", st retchy = \"false\", symmetric = \"false\", largeop = \"false\", movabl elimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+ \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x \", italic = \"true\", mathvariant = \"italic\")), mathvariant = \"nor mal\")), Typesetting:-mn(\"5\", mathvariant = \"normal\"), superscript shift = \"0\")), Typesetting:-mo(\"+\", mathvariant = \"normal\", fenc e = \"false\", separator = \"false\", stretchy = \"false\", symmetric \+ = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typese tting:-mrow(Typesetting:-msup(Typesetting:-mrow(Typesetting:-mi(\"sin \", italic = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\"& ApplyFunction;\", mathvariant = \"normal\", fence = \"false\", separat or = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(T ypesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), m athvariant = \"normal\")), Typesetting:-mn(\"4\", mathvariant = \"norm al\"), superscriptshift = \"0\")), Typesetting:-mo(\"+\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.22 22222em\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"n ormal\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mrow(Typesetting:-msup(Typesetting:-mrow(Typesetting:-mi(\"cos\", i talic = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\"&Apply Function;\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em \", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typese tting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathva riant = \"normal\")), Typesetting:-mn(\"2\", mathvariant = \"normal\") , superscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"−\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.22 22222em\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"n ormal\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mrow(Typesetting:-msup(Typesetting:-mrow(Typesetting:-mi(\"sin\", i talic = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\"&Apply Function;\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em \", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typese tting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), mathva riant = \"normal\")), Typesetting:-mn(\"2\", mathvariant = \"normal\") , superscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"−\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.22 22222em\"), Typesetting:-mrow(Typesetting:-mi(\"cos\", italic = \"fals e\", mathvariant = \"normal\"), Typesetting:-mo(\"⁡\", m athvariant = \"normal\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+ \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\" \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Ty pesetting:-mn(\"2\", mathvariant = \"normal\"), Typesetting:-mo(\"&Inv isibleTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .0em\", rspace = \"0.0em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", \+ mathvariant = \"italic\")), mathvariant = \"normal\")), Typesetting:-m i(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mi (\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+m odulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%tru eF'/%,mathvariantGQ'italicF'-F#6-F+-F#6#-I%msupGF$6%-F#6%-F,6%Q$cosF'/ F0Q&falseF'/F3Q'normalF'-I#moGF$6-Q0⁡F'FC/%&fenceGFB/%*s eparatorGFB/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsG FB/%'accentGFB/%'lspaceGQ&0.0emF'/%'rspaceGFY-I(mfencedGF$6$-F#6#-F,6% Q\"xF'F/F2FC-I#mnGF$6$Q\"5F'FC/%1superscriptshiftGQ\"0F'-FF6-Q\"+F'FCF IFKFMFOFQFSFU/FXQ,0.2222222emF'/FenFio-F#6#-F:6%-F#6%-F,6%Q$sinF'FAFCF EFfn-F_o6$Q\"4F'FCFboFeo-F#6&-F_o6$Q\"2F'FC-FF6-Q1⁢F'FC FIFKFMFOFQFSFUFWFZ-F#6#-F:6%FFE-Fgn6$-F#6%F+-F#6%F ipF\\qF[oF+FCF+F+" }{TEXT 251 4 " . " }}{EXCHG {PARA 0 "> " 0 "simpli fy" {MPLTEXT 1 0 69 "simplify( cos(x)^5 + sin(x)^4 + 2*cos(x)^2 - 2*si n(x)^2 - cos(2*x) );" }}}{PARA 0 "" 0 "" {TEXT 251 41 "Press [Enter] t o simplify the expression." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 50 "Another way to simplify expressions is to use t he " }{TEXT 232 6 "normal" }{TEXT 251 117 " command, which puts fracti ons on a common denominator and removes common factors in the numerato r and denominator. " }}{PARA 0 "" 0 "" {TEXT 251 13 "The fraction " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mrow( Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Ty pesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"3 \", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting :-mo(\"−\", mathvariant = \"normal\", fence = \"false\", separat or = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesettin g:-msup(Typesetting:-mi(\"y\", italic = \"true\", mathvariant = \"ital ic\"), Typesetting:-mn(\"3\", mathvariant = \"normal\"), superscriptsh ift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+ \"italic\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+ \"italic\")), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Types etting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \+ \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), supersc riptshift = \"0\")), Typesetting:-mo(\"+\", mathvariant = \"normal\", \+ fence = \"false\", separator = \"false\", stretchy = \"false\", symmet ric = \"false\", largeop = \"false\", movablelimits = \"false\", accen t = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Ty pesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typ esetting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp ace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi(\"y \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&m inus;\", mathvariant = \"normal\", fence = \"false\", separator = \"fa lse\", stretchy = \"false\", symmetric = \"false\", largeop = \"false \", movablelimits = \"false\", accent = \"false\", lspace = \"0.222222 2em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-msup( Typesetting:-mi(\"y\", italic = \"true\", mathvariant = \"italic\"), T ypesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \" 0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \")), linethickness = \"1\", denomalign = \"center\", numalign = \"cen ter\", bevelled = \"false\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6#-I&mfracGF$6(-F#6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/% ,mathvariantGQ'italicF'-F#6'F0-F#6#-I%msupGF$6%-F16%Q\"xF'F4F7-I#mnGF$ 6$Q\"3F'/F8Q'normalF'/%1superscriptshiftGQ\"0F'-I#moGF$6-Q(−F'FH /%&fenceGQ&falseF'/%*separatorGFS/%)stretchyGFS/%*symmetricGFS/%(large opGFS/%.movablelimitsGFS/%'accentGFS/%'lspaceGQ,0.2222222emF'/%'rspace GF\\o-F#6#-F?6%-F16%Q\"yF'F4F7FDFJF0F0-F#6%F0-F#6+F0-F#6#-F?6%FA-FE6$Q \"2F'FHFJ-FN6-Q\"+F'FHFQFTFVFXFZFfnFhnFjnF]oFAFMFcoFM-F#6#-F?6%FcoF^pF JF0F0/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF]q/%) bevelledGFS" }{TEXT 251 57 " is much simpler after Maple removes the \+ common factors." }}{EXCHG {PARA 0 "> " 0 "normal" {MPLTEXT 1 0 34 "nor mal( (x^3-y^3)/(x^2+x-y-y^2) );" }}}{PARA 0 "" 0 "" {TEXT 251 40 "Pres s ENTER to normalize the expression." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 254 24 "Assigning \+ Variable names" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 154 "The use of variables is essential for managing large nu mbers of expressions and functions, especially if you want to reuse th e output later in a session. " }}{PARA 0 "" 0 "" {TEXT 251 44 "For exa mple, define an expression such as, " }{XPPEDIT 18 0 "Typesetting:-mr ow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mfenced(Typesetting: -mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \"), Typesetting:-mrow(Typesetting:-mn(\"41\", mathvariant = \"normal \"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mr ow(Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvar iant = \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), \+ superscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", m athvariant = \"italic\")), Typesetting:-mo(\"+\", mathvariant = \"norm al\", fence = \"false\", separator = \"false\", stretchy = \"false\", \+ symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em \"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic \"), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn( \"1\", mathvariant = \"normal\")), mathvariant = \"normal\"), Typesett ing:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\"), T ypesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced (Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvarian t = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mathvariant \+ = \"normal\"), Typesetting:-mo(\"⁢\", mathvariant = \"n ormal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Type setting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), Type setting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\", \+ separator = \"false\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"1\" , mathvariant = \"normal\")), mathvariant = \"normal\")), Typesetting: -mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/ I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ% trueF'/%,mathvariantGQ'italicF'-F#6%-I%msupGF$6%-I(mfencedGF$6$-F#6(F+ -F#6&-I#mnGF$6$Q#41F'/F3Q'normalF'-I#moGF$6-Q1⁢F'FE/%&f enceGQ&falseF'/%*separatorGFM/%)stretchyGFM/%*symmetricGFM/%(largeopGF M/%.movablelimitsGFM/%'accentGFM/%'lspaceGQ&0.0emF'/%'rspaceGFfn-F#6#- F86%-F,6%Q\"xF'F/F2-FB6$Q\"2F'FE/%1superscriptshiftGQ\"0F'F+-FH6-Q\"+F 'FEFKFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFjoF]oFfo-FB6$Q\"1F'FEFEF`oFco FG-F;6$-F#6&F+-F#6%F`oFGF]o-FH6-Q(−F'FEFKFNFPFRFTFVFXFioF[pF\\pF EF+" }{TEXT 251 18 ", and store it as " }{XPPEDIT 18 0 "Typesetting:-m row(Typesetting:-mi(\"expr1\", italic = \"true\", mathvariant = \"ital ic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#mi GF$6%Q&expr1F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'" }{TEXT 251 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "expr1 := (41*x^2+x+1 )^2*(2*x-1);" }}}{PARA 0 "" 0 "" {TEXT 251 34 "Press ENTER to see the \+ expression." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 8 "Use the " }{TEXT 233 6 "expand" }{TEXT 200 1 " " }{TEXT 251 11 "command on " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"expr 1\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+mod ulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q&expr1F'/%'italicGQ% trueF'/%,mathvariantGQ'italicF'" }{TEXT 251 37 " and store the result \+ as a variable, " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"e xpr2\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+ modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q&expr2F'/%'italic GQ%trueF'/%,mathvariantGQ'italicF'" }{TEXT 251 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "expr2 := expand(expr1);" }}}{PARA 0 "" 0 "" {TEXT 251 37 "Press ENTER to expand the expression." }}{PARA 0 "" 0 " " {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 17 "You can evaluate " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"expr2\", italic = \+ \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,T ypesettingGI(_syslibGF'6#-I#miGF$6%Q&expr2F'/%'italicGQ%trueF'/%,mathv ariantGQ'italicF'" }{TEXT 251 5 " at " }{TEXT 234 1 "x" }{TEXT 251 3 "=1." }}{EXCHG {PARA 0 "> " 0 "eval" {MPLTEXT 1 0 19 "eval(expr2 , x=1 );" }}}{PARA 0 "" 0 "" {TEXT 251 50 "Press ENTER to see the results o f this evaluation." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 42 "There is another way to evaluate expr2 at " }{TEXT 235 1 "x" }{TEXT 251 5 " = 1." }}{EXCHG {PARA 0 "> " 0 "subs" {MPLTEXT 1 0 16 "subs(x=1,expr2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 254 17 "Solving Equations" }}{SECT 1 {PARA 0 "" 0 "" {TEXT 206 19 "Alg ebraic equations" }}{PARA 0 "" 0 "" {TEXT 251 55 "Use Maple to solve t he following algebraic equation: " }{XPPEDIT 18 0 "Typesetting:-mrow (Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), T ypesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant \+ = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"2\" , mathvariant = \"normal\"), Typesetting:-mo(\"⁢\", mat hvariant = \"normal\", fence = \"false\", separator = \"false\", stret chy = \"false\", symmetric = \"false\", largeop = \"false\", movableli mits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0 .0em\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", it alic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"3\", mat hvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\" \", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"+ \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-msup(Typese tting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typeset ting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), \+ Typesetting:-mo(\"=\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mrow(Types etting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typeset ting:-mrow(Typesetting:-mn(\"25\", mathvariant = \"normal\"), Typesett ing:-mo(\"⁢\", mathvariant = \"normal\", fence = \"fals e\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"x\", ital ic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"−\" , mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+ stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", r space = \"0.2222222em\"), Typesetting:-mn(\"12\", mathvariant = \"norm al\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"itali c\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic \"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF $6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6'F+-F#6'F+-F#6&- I#mnGF$6$Q\"2F'/F3Q'normalF'-I#moGF$6-Q1⁢F'F?/%&fenceGQ &falseF'/%*separatorGFG/%)stretchyGFG/%*symmetricGFG/%(largeopGFG/%.mo vablelimitsGFG/%'accentGFG/%'lspaceGQ&0.0emF'/%'rspaceGFV-F#6#-I%msupG F$6%-F,6%Q\"xF'F/F2-F<6$Q\"3F'F?/%1superscriptshiftGQ\"0F'F+-FB6-Q\"+F 'F?FEFHFJFLFNFPFR/FUQ,0.2222222emF'/FXFeo-F#6#-Ffn6%FhnF;F^oF+-FB6-Q\" =F'F?FEFHFJFLFNFPFR/FUQ,0.2777778emF'/FXF_p-F#6&F+-F#6%-F<6$Q#25F'F?FA Fhn-FB6-Q(−F'F?FEFHFJFLFNFPFRFdoFfo-F<6$Q#12F'F?F+F+" }{TEXT 251 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eqn := 2*x^3+x^ 2 = 25*x-12;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve( eqn, \{x\} ) ;" }}}{PARA 0 "" 0 "" {TEXT 251 31 "Press ENTER to see the results." } }{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 82 "To ver ify that this is a solution, evaluate the equation at a particular val ue of " }{TEXT 236 1 "x" }{TEXT 251 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eval( eqn , x=3);" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 41 "You can also solve the equation direct ly." }}{EXCHG {PARA 0 "> " 0 "solve" {MPLTEXT 1 0 29 "solve(2*x^3+x^2 \+ = 25*x-12,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 206 20 "Syst ems of equations" }{TEXT 237 0 "" }}{PARA 0 "" 0 "" {TEXT 251 50 "You \+ can also solve systems of equations in Maple. " }}{PARA 0 "" 0 "" {TEXT 251 65 "Consider the following set of three equations and three \+ unknowns:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eqn1 := x+2*y-2 *z=-2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eqn2 := 5*x+9*y-4*z=-3;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eqn3 := 3*x+4*y-5*z=-3;" }}} {PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 39 "Now sol ve the system for the variables " }{XPPEDIT 18 0 "Typesetting:-mrow(Ty pesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"));" " -I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q\"xF '/%'italicGQ%trueF'/%,mathvariantGQ'italicF'" }{TEXT 251 2 ", " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"y\", italic = \"tru e\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,Typese ttingGI(_syslibGF'6#-I#miGF$6%Q\"yF'/%'italicGQ%trueF'/%,mathvariantGQ 'italicF'" }{TEXT 251 6 ", and " }{XPPEDIT 18 0 "Typesetting:-mrow(Typ esetting:-mi(\"z\", italic = \"true\", mathvariant = \"italic\"));" "- I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6%Q\"zF' /%'italicGQ%trueF'/%,mathvariantGQ'italicF'" }{TEXT 251 3 ". " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solve( \{eqn1, eqn2, eqn3\}, \{x, y, z\} );" }}}{PARA 0 "" 0 "" {TEXT 251 31 "Press ENTER to see t he results." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 44 "To verify that this solution satisfies, say " }{TEXT 19 4 "eqn 1" }{TEXT 251 5 " and " }{TEXT 19 4 "eqn2" }{TEXT 251 43 " , evaluate \+ both of them at this solution. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eval( \{eqn1, eqn2\} , % );" }}}{PARA 0 "" 0 "" {TEXT 251 31 " Press ENTER to see the results." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 8 "Graphics" }}{PARA 0 "" 0 "" {TEXT 251 57 "The following examples generate and refine the gra ph of " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", itali c = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting :-mi(\"y\", italic = \"true\", mathvariant = \"italic\"), Typesetting: -mo(\"=\", mathvariant = \"normal\", fence = \"false\", separator = \" false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.27777 78em\", rspace = \"0.2777778em\"), Typesetting:-mrow(Typesetting:-msup (Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), \+ Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \+ \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"ital ic\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"itali c\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miG F$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6&-F,6%Q\"yF'F/F 2-I#moGF$6-Q\"=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)stre tchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%'l spaceGQ,0.2777778emF'/%'rspaceGFQ-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2-I#mn GF$6$Q\"2F'F>/%1superscriptshiftGQ\"0F'F+F+" }{TEXT 251 1 "." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "p lot(x^2,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(x^2,x=- 5..5,y=0..25);" }}}{PARA 0 "" 0 "" {TEXT 251 83 "Note that in the last graph, the domain and range of the function were specified. " }} {PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 142 "The ne xt example demonstrates how to plot more than one function on the same plane. We first define two new functions (as maple expressions)." }} {PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "m:=x^3-9*x^2+26*x-24;" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "n:=3*x^2-11*x+6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(\{m,n\},x=-1..8);" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 92 "We can find the x-coordinates of the points of intersection of m and n in the followi ng way." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(m=n,x);" } {TEXT 251 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 67 "We can also find decim al approximations of the intersections using " }{TEXT 238 6 "fsolve" } {TEXT 251 1 "." }}{EXCHG {PARA 0 "> " 0 "fsolve" {MPLTEXT 1 0 14 "fsol ve(m=n,x);" }{TEXT 251 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 84 "Next we f ind find the y-coordinate associated with intersection coordinate of x = 3." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eval(m,x=3);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 251 61 "Thus, (3,0) is a point of interse ction between the graphs of " }{TEXT 239 1 "m" }{TEXT 251 5 " and " } {TEXT 240 1 "n" }{TEXT 251 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 253 16 "Lab Assignment 1" } }{PARA 0 "" 0 "" {TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 728 "Do yo ur lab in a new file (go to the file menu and click on \"New\"). Copy and paste the below questions to your new file. Be sure to start you r lab by putting your name on the first line. Here's a way to do that: Look at the icon bar at the top of the screen and you will see a T bu tton in the center. Clicking on that T puts you in text mode (i.e. you can write whatever you want and Maple will ignore it.) Clicking on t he arrow button just to the right of the T lets you return to calculat ion mode (i.e. Maple knows to evaluate lines that start with this arro w). Use Maple to answer the questions. ANSWER ALL QUESTIONS COMPLETE LY IF YOU WANT FULL CREDIT!!! When you complete the lab, hand in a pr intout of your worksheet." }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 251 37 "1. Expand the following expressions." } }{PARA 0 "" 0 "" {TEXT 251 3 "a) " }{XPPEDIT 18 0 "Typesetting:-mrow(T ypesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typ esetting:-mrow(Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mro w(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"), \+ Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", italic = \" true\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", mathvariant \+ = \"normal\"), superscriptshift = \"0\")), Typesetting:-mo(\"+\", math variant = \"normal\", fence = \"false\", separator = \"false\", stretc hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace \+ = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mathvaria nt = \"normal\"), Typesetting:-mo(\"⁢\", mathvariant = \+ \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Ty pesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), Ty pesetting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\" , separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls pace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"1 \", mathvariant = \"normal\")), mathvariant = \"normal\"), Typesetting :-mn(\"3\", mathvariant = \"normal\"), superscriptshift = \"0\"), Type setting:-mo(\"⁢\", mathvariant = \"normal\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typ esetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+ \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\" , italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-m o(\"−\", mathvariant = \"normal\", fence = \"false\", separator \+ = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \" false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2 222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"2\", mathvari ant = \"normal\")), mathvariant = \"normal\")), Typesetting:-mi(\"\", \+ italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulena meG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,m athvariantGQ'italicF'-F#6%-I%msupGF$6%-I(mfencedGF$6$-F#6(F+-F#6#-F86% -F,6%Q\"xF'F/F2-I#mnGF$6$Q\"2F'/F3Q'normalF'/%1superscriptshiftGQ\"0F' -I#moGF$6-Q\"+F'FJ/%&fenceGQ&falseF'/%*separatorGFU/%)stretchyGFU/%*sy mmetricGFU/%(largeopGFU/%.movablelimitsGFU/%'accentGFU/%'lspaceGQ,0.22 22222emF'/%'rspaceGF^o-F#6%FF-FP6-Q1⁢F'FJFSFVFXFZFfnFhn Fjn/F]oQ&0.0emF'/F`oFgoFC-FP6-Q(−F'FJFSFVFXFZFfnFhnFjnF\\oF_o-FG 6$Q\"1F'FJFJ-FG6$Q\"3F'FJFLFco-F;6$-F#6&F+F?FioFFFJF+" }{TEXT 251 44 " " }}{PARA 0 "" 0 "" {TEXT 251 4 "b) " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", i talic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Typeset ting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"+ \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi(\"a\", italic = \"true\", \+ mathvariant = \"italic\")), mathvariant = \"normal\"), Typesetting:-mn (\"5\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typeset ting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mro wG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'ital icGQ%trueF'/%,mathvariantGQ'italicF'-F#6#-I%msupGF$6%-I(mfencedGF$6$-F #6%-F,6%Q\"xF'F/F2-I#moGF$6-Q\"+F'/F3Q'normalF'/%&fenceGQ&falseF'/%*se paratorGFJ/%)stretchyGFJ/%*symmetricGFJ/%(largeopGFJ/%.movablelimitsGF J/%'accentGFJ/%'lspaceGQ,0.2222222emF'/%'rspaceGFY-F,6%Q\"aF'F/F2FF-I# mnGF$6$Q\"5F'FF/%1superscriptshiftGQ\"0F'F+" }{TEXT 251 0 "" }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 251 13 "2. Factor: " }{XPPEDIT 18 0 "Typesetti ng:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"ital ic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", math variant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting :-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typesetting: -mn(\"8\", mathvariant = \"normal\"), superscriptshift = \"0\")), Type setting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\", \+ separator = \"false\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"1\" , mathvariant = \"normal\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesettin gGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ'itali cF'-F#6&F+-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2-I#mnGF$6$Q\"8F'/F3Q'normalF '/%1superscriptshiftGQ\"0F'-I#moGF$6-Q(−F'FC/%&fenceGQ&falseF'/% *separatorGFN/%)stretchyGFN/%*symmetricGFN/%(largeopGFN/%.movablelimit sGFN/%'accentGFN/%'lspaceGQ,0.2222222emF'/%'rspaceGFgn-F@6$Q\"1F'FCF+" }{TEXT 251 0 "" }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 251 59 "3. Add the following rational expressions by appl ying the " }{TEXT 241 8 "simplify" }{TEXT 251 10 " command: " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mfrac(Ty pesetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \"normal\"), Type setting:-mo(\"⁢\", mathvariant = \"normal\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mrow(Typese tting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \" italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscri ptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", mathvarian t = \"italic\")), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"t rue\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\" \", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow(Ty pesetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant \+ = \"italic\"), Typesetting:-mn(\"3\", mathvariant = \"normal\"), super scriptshift = \"0\")), Typesetting:-mo(\"−\", mathvariant = \"no rmal\", fence = \"false\", separator = \"false\", stretchy = \"false\" , symmetric = \"false\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222 em\"), Typesetting:-mn(\"1\", mathvariant = \"normal\")), Typesetting: -mi(\"\", italic = \"true\", mathvariant = \"italic\")), linethickness = \"1\", denomalign = \"center\", numalign = \"center\", bevelled = \+ \"false\"), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \+ \"false\", separator = \"false\", stretchy = \"false\", symmetric = \" false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesettin g:-mfrac(Typesetting:-mrow(Typesetting:-mn(\"3\", mathvariant = \"norm al\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symme tric = \"false\", largeop = \"false\", movablelimits = \"false\", acce nt = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:- mi(\"x\", italic = \"true\", mathvariant = \"italic\")), Typesetting:- mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\" ), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvari ant = \"italic\"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi (\"x\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn( \"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesett ing:-mo(\"−\", mathvariant = \"normal\", fence = \"false\", sepa rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"1\", ma thvariant = \"normal\")), Typesetting:-mi(\"\", italic = \"true\", mat hvariant = \"italic\")), linethickness = \"1\", denomalign = \"center \", numalign = \"center\", bevelled = \"false\")), Typesetting:-mi(\" \", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modu lenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF' /%,mathvariantGQ'italicF'-F#6%-I&mfracGF$6(-F#6&-I#mnGF$6$Q\"2F'/F3Q'n ormalF'-I#moGF$6-Q1⁢F'F@/%&fenceGQ&falseF'/%*separatorG FH/%)stretchyGFH/%*symmetricGFH/%(largeopGFH/%.movablelimitsGFH/%'acce ntGFH/%'lspaceGQ&0.0emF'/%'rspaceGFW-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2F< /%1superscriptshiftGQ\"0F'F+-F#6%F+-F#6&F+-F#6#-Fgn6%Fin-F=6$Q\"3F'F@F \\o-FC6-Q(−F'F@FFFIFKFMFOFQFS/FVQ,0.2222222emF'/FYF^p-F=6$Q\"1F' F@F+/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFhp/%)b evelledGFH-FC6-Q\"+F'F@FFFIFKFMFOFQFSF]pF_p-F86(-F#6%FgoFBFin-F#6%F+-F #6&F+FZFjoF`pF+FcpFfpFipF[qF+" }{TEXT 251 2 " ." }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 251 37 "4. Input the fo llowing polynomials: " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:- mi(\"\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mr ow(Typesetting:-mi(\"p\", italic = \"true\", mathvariant = \"italic\") , Typesetting:-mo(\"=\", mathvariant = \"normal\", fence = \"false\", \+ separator = \"false\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mrow(Typ esetting:-mo(\"&uminus0;\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow (Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvaria nt = \"italic\"), Typesetting:-mn(\"4\", mathvariant = \"normal\"), su perscriptshift = \"0\")), Typesetting:-mo(\"+\", mathvariant = \"norma l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\" ), Typesetting:-mrow(Typesetting:-mn(\"4\", mathvariant = \"normal\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mrow( Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvarian t = \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), sup erscriptshift = \"0\")), Typesetting:-mi(\"\", italic = \"true\", math variant = \"italic\")), Typesetting:-mo(\"+\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\") , Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")) , Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F '/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F#6&-F,6%Q\"pF'F/F2-I#moG F$6-Q\"=F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)stretchyGFB /%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%'lspaceGQ ,0.2777778emF'/%'rspaceGFQ-F#6(-F;6-Q*&uminus0;F'F>F@FCFEFGFIFKFM/FPQ, 0.2222222emF'/FSFZ-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2-I#mnGF$6$Q\"4F'F>/% 1superscriptshiftGQ\"0F'-F;6-Q\"+F'F>F@FCFEFGFIFKFMFYFen-F#6&F^o-F;6-Q 1⁢F'F>F@FCFEFGFIFKFM/FPQ&0.0emF'/FSF^p-F#6#-Fin6%F[o-F_ o6$Q\"2F'F>FboF+FeoF[oF+F+" }{TEXT 251 6 " and " }{XPPEDIT 18 0 "Type setting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathvariant = \+ \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"q\", italic = \"true \", mathvariant = \"italic\"), Typesetting:-mo(\"=\", mathvariant = \" normal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.277777 8em\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mat hvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"3\", mathv ariant = \"normal\"), Typesetting:-mo(\"⁢\", mathvarian t = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\" ), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", mathvaria nt = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\"\", it alic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"− \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mn(\"11\", \+ mathvariant = \"normal\"), Typesetting:-mo(\"⁢\", mathv ariant = \"normal\", fence = \"false\", separator = \"false\", stretch y = \"false\", symmetric = \"false\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0 em\"), Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"itali c\")), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"fals e\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn (\"6\", mathvariant = \"normal\")), Typesetting:-mi(\"\", italic = \"t rue\", mathvariant = \"italic\")), Typesetting:-mi(\"\", italic = \"tr ue\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvariantGQ' italicF'-F#6&-F,6%Q\"qF'F/F2-I#moGF$6-Q\"=F'/F3Q'normalF'/%&fenceGQ&fa lseF'/%*separatorGFB/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movab lelimitsGFB/%'accentGFB/%'lspaceGQ,0.2777778emF'/%'rspaceGFQ-F#6(F+-F# 6&-I#mnGF$6$Q\"3F'F>-F;6-Q1⁢F'F>F@FCFEFGFIFKFM/FPQ&0.0e mF'/FSFjn-F#6#-I%msupGF$6%-F,6%Q\"xF'F/F2-FY6$Q\"2F'F>/%1superscriptsh iftGQ\"0F'F+-F;6-Q(−F'F>F@FCFEFGFIFKFM/FPQ,0.2222222emF'/FSF^p-F #6%-FY6$Q#11F'F>FfnFao-F;6-Q\"+F'F>F@FCFEFGFIFKFMF]pF_p-FY6$Q\"6F'F>F+ F+" }{TEXT 251 38 " (for example, assign the polynomial " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"true\", mathv ariant = \"italic\"), Typesetting:-mrow(Typesetting:-mo(\"&uminus0;\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", s tretchy = \"false\", symmetric = \"false\", largeop = \"false\", movab lelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rs pace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-msup(Typesetti ng:-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typesettin g:-mn(\"4\", mathvariant = \"normal\"), superscriptshift = \"0\")), Ty pesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", sepa rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typeset ting:-mn(\"4\", mathvariant = \"normal\"), Typesetting:-mo(\"&Invisibl eTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \" false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\" , rspace = \"0.0em\"), Typesetting:-mrow(Typesetting:-msup(Typesetting :-mi(\"x\", italic = \"true\", mathvariant = \"italic\"), Typesetting: -mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Type setting:-mi(\"\", italic = \"true\", mathvariant = \"italic\")), Types etting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separat or = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \" 0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi(\"x\", itali c = \"true\", mathvariant = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", mathvariant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\" I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q!F'/%'italicGQ%trueF'/%,mathvar iantGQ'italicF'-F#6(-I#moGF$6-Q*&uminus0;F'/F3Q'normalF'/%&fenceGQ&fal seF'/%*separatorGF?/%)stretchyGF?/%*symmetricGF?/%(largeopGF?/%.movabl elimitsGF?/%'accentGF?/%'lspaceGQ,0.2222222emF'/%'rspaceGFN-F#6#-I%msu pGF$6%-F,6%Q\"xF'F/F2-I#mnGF$6$Q\"4F'F;/%1superscriptshiftGQ\"0F'-F86- Q\"+F'F;F=F@FBFDFFFHFJFLFO-F#6&FY-F86-Q1⁢F'F;F=F@FBFDFF FHFJ/FMQ&0.0emF'/FPFco-F#6#-FT6%FV-FZ6$Q\"2F'F;FgnF+FjnFVF+" }{TEXT 251 10 " the name " }{TEXT 242 1 "p" }{TEXT 251 224 "). Next, graph t he polynomials on the same coordinate axes. Adjust the domain and rang e appropriately so you can estimate the intersection points of the pol ynomials. What is an approximation for the points of intersection?" } }}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 251 56 "5. Find the roots (a.k.a. the zeros) of the polynomial " }{TEXT 243 1 "q" }{TEXT 251 12 " by setting " }{TEXT 244 1 "q" }{TEXT 251 32 " equal to zero and applying the " }{TEXT 245 5 "solve" }{TEXT 251 10 " command. " }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 251 87 "6. Estimate the points of intersection of the two pol ynomials defined above using the " }{TEXT 246 6 "fsolve" }{TEXT 251 21 " command to find the " }{TEXT 247 8 " x" }{TEXT 251 17 "-coo rdinates and " }{TEXT 248 4 "eval" }{TEXT 251 4 " or " }{TEXT 249 4 "s ubs" }{TEXT 251 27 " to find the corresponding " }{TEXT 250 1 "y" } {TEXT 251 13 "-coordinates." }}}{PARA 0 "" 0 "" {TEXT 251 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT 251 22 "7. Find the value of " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"π\", italic = \" false\", mathvariant = \"normal\"));" "-I%mrowG6#/I+modulenameG6\"I,Ty pesettingGI(_syslibGF'6#-I#miGF$6%Q%πF'/%'italicGQ&falseF'/%,mathva riantGQ'normalF'" }{TEXT 251 40 " correct to 100 places past the decim al." }}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }