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Maple's ability to produce exact answers in addition to numerical approximations gives y ou more options in solving problems." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 33 "Doing Exact Arithmetic with Maple" }}{PARA 0 "" 0 "" {TEXT -1 126 "Using Maple to do numerical computations is very straightforward. Just enter the numerical expression and end the line with a " }{TEXT 262 9 "semicolon" }{TEXT -1 11 ". Pressing " }{TEXT 263 7 "[Enter]" } {TEXT -1 97 " will then execute the line and the result will be displa yed in blue in the center of the screen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 283 10 "Example 1:" }}{PARA 0 "" 0 "" {TEXT -1 97 "A simple calculation has been entered on the next line. C lick anywhere in the red line and press " }{TEXT 264 7 "[Enter]" } {TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+4;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "12*34567890;" }}}{PARA 0 "" 0 "" {TEXT -1 63 "Each red input line is \"live\" and can be modified \+ at any time. " }}{PARA 0 "" 0 "" {TEXT -1 53 "Change the \"4\" in the \+ line above to an \"8\" and press " }{TEXT 311 7 "[Enter]" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 79 "Notice how the blue output is auto matically updated to display the new result. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 284 10 "Example 2:" }}{PARA 0 " " 0 "" {TEXT -1 37 "For our next example let's calculate " }{XPPEDIT 18 0 "134^39" "6#*$\"$M\"\"#R" }{TEXT -1 3 ". " }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 7 "134^39;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 96 "Unlike your calculator, Maple gives you the exact answer to this problem, all 83 digits worth! " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 285 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 66 "Maple can calculate with fractions without converting to decimals:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "3/5 + 5/9 + 7/12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 286 10 "Ex ample 4:" }}{PARA 0 "" 0 "" {TEXT -1 51 "To enter the square root of a number use sqrt( ) :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqr t(24);" }}}{PARA 0 "" 0 "" {TEXT -1 34 "Notice that Maple has simplifi ed " }{XPPEDIT 18 0 "sqrt(24)" "6#-%%sqrtG6#\"#C" }{TEXT -1 126 " but has left the answer in exact form. In the next section you will learn how to get a decimal approximation for this number." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 287 10 "Example 5:" }}{PARA 0 "" 0 "" {TEXT -1 73 "Maple has all of the important mathematical const ants built in. To enter " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT -1 12 " type Pi. " }}{PARA 0 "" 0 "" {TEXT -1 65 "Notice that an asterisk * is required to indicate multiplication." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "4*(3+Pi);" }}}{PARA 0 "" 0 "" {TEXT -1 77 "Again Maple carries out the calculation but leaves the answer in exact form. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 290 10 "Example \+ 6:" }}{PARA 0 "" 0 "" {TEXT -1 95 "Unlike your calculator, Maple gives you the exact answer when applying trigonometric functions." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s in(5*Pi/3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sec(Pi/4);" }}}{PARA 0 "" 0 "" {TEXT -1 44 "To get the inverse sine of a number us e the " }{TEXT 297 9 "arcsin( )" }{TEXT -1 10 " function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "arcsin(-1);" }}}{PARA 0 "" 0 "" {TEXT -1 46 "If you ask Maple to calculate a value that is " }{TEXT 309 9 "undefined" }{TEXT -1 39 " it will respond with an error message :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tan(Pi/2);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 289 10 "Example 7:" }} {PARA 0 "" 0 "" {TEXT -1 43 "To enter the natural exponential function " }{XPPEDIT 18 0 "exp(x)" "6#-%$expG6#%\"xG" }{TEXT -1 27 " in Mapl e type: exp(x) . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(x); " }}}{PARA 0 "" 0 "" {TEXT -1 49 "And to get the number e by itself ty pe: exp(1) ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 295 10 "Example 8:" }}{PARA 0 "" 0 "" {TEXT -1 37 "To enter the absolu te value function " }{XPPEDIT 18 0 "abs(x)" "6#-%$absG6#%\"xG" }{TEXT -1 25 " in Maple type: abs(x). " }}{PARA 0 "" 0 "" {TEXT -1 75 "Note \+ that Maple gives the correct, exact answer for the third line since: \+ " }{XPPEDIT 18 0 "exp(1)-Pi < 0" "6#2,&-%$expG6#\"\"\"\"\"\"%#PiG!\"\" \"\"!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "abs(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "abs(-3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "abs(exp(1)-Pi);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 288 10 "Example 9:" }}{PARA 0 "" 0 "" {TEXT -1 235 "Maple has many special purpose commands for working with numbers. You will learn these as you need them in your math course. Here is on e last example for now. If we have an integer and want to factor it in to primes we can use Maple's " }{TEXT 257 11 "ifactor( )" }{TEXT -1 59 " command. Feel free to experiment by changing the number. " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ifactor(31722722304);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 307 11 "Example 10:" }}{PARA 0 "" 0 "" {TEXT -1 131 "There may be time s when you want to enter more than one command on a single line. This \+ is okay to do in Maple, just be sure to end " }{TEXT 308 4 "each" } {TEXT -1 92 " command with a semicolon. It also helps to put spaces be tween the commands. When you press " }{TEXT 310 7 "[Enter]" }{TEXT -1 100 " all of the expressions are executed and the results are listed, \+ in order, in a single output field." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sin(Pi/3); cos(Pi/3); t an(Pi/3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 " " 0 "" {TEXT 313 11 "Example 11:" }}{PARA 0 "" 0 "" {TEXT -1 55 "To ca lculate and display a sequence of numbers use the " }{TEXT 314 7 "seq( ..)" }{TEXT -1 73 " command. Here we calculate the squares of the firs t 100 natural numbers." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "se q(k^2,k=1..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "evalf( )" {TEXT -1 35 "Numerical Approximations using the " }{TEXT 299 8 "evalf( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT -1 248 "Recall that in the previous section we asked Maple to add three fractions and the result was also displayed as a fraction. This sort of exact arithmeti c is very useful but there are times when we prefer an answer in decim al form. The Maple command " }{TEXT 258 11 " evalf( )" }{TEXT -1 29 " performs this task for us. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 292 10 "Example 1:" }}{PARA 0 "" 0 "" {TEXT -1 42 "Compare the results of the next two lines." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "3/5+5/9+7/12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(3/5+5/9+7/12);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 291 10 "Example 2:" }} {PARA 0 "" 0 "" {TEXT -1 138 "Assigning a name to the result of a calc ulation makes it easier to use that result in a subsequent calculation . To assign a name we use a " }{TEXT 293 5 "colon" }{TEXT -1 147 " fol lowed by an equal sign ( i.e. name := result ; ) . On the next line w e have assigned the letter k to the original output above. Then we app ly " }{XPPEDIT 18 0 "evalf( )" "6#-%&evalfG6\"" }{TEXT -1 8 " to k. \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "k:=3/5+5/9+7/12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " evalf(k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 " " 0 "" {TEXT 296 20 "Important Maple Note" }{TEXT -1 95 ": Maple is ca se sensitive. So for example Maple considers k and K to be different \+ variables.. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "k;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "K;" }}}{PARA 0 "" 0 "" {TEXT -1 53 "By the way you can also use words as variable names. " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "joe:=2^5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(joe);" }}}{PARA 0 "" 0 "" {TEXT 294 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 123 "If we want fewer or mo re digits of accuracy than the default number which is 10 digits we ca n add an extra argument to the " }{TEXT 312 9 "evalf( )" }{TEXT -1 25 " command as shown below. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "w:=4*(3+Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(w);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(w,4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(w,45);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{PARA 0 "" 0 "" {TEXT 298 10 "Example 4:" }{TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 129 "If you enter numbers with a decimal point Mapl e automatically gives decimal results. Compare the results of the two \+ lines below. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(34);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(34.0);" }}}{PARA 0 " " 0 "" {TEXT -1 24 "Here is another example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "4-1/3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "4.0-1/3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }{TEXT 315 10 "Example 5:" }}{PARA 0 "" 0 "" {TEXT -1 190 "We can apply the evalf( ) command to a sequence of numb ers. Below we first generate the exact square roots of the first 10 n atural numbers, then apply evalf to get decimal approximations. " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "result:=seq(sqrt(k),k=1..10) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(result);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 46 "Maple Shortcut: Quick referenc e to last output" }}{PARA 0 "" 0 "" {TEXT -1 209 "There will be many t imes when using Maple that you will string together a sequence of comp utations. Rather than giving a name to each result as you go along, yo u can use the percent sign ( % ) to refer to the " }{TEXT 260 34 "last expression computed by Maple." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 40 "Here are some examples of how it works. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "3/5+5/9+7 /12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%+5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 237 "Be careful when \+ using the ditto symbol, it refers to the last output calculated, not n ecessarily the line above it .\nIt is safer to use labels instead, or \+ get into the habit of only using the % on the same line as the object \+ referred to." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "3/5+5/9+7/12; evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Pi; evalf(%); % + 5;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "or" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ans1 := 3/5+ 5/9+7/12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(ans1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ans2 := evalf(Pi);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ans2+5;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "For more on using the dit to symbol see " }{TEXT 280 12 "Exercise 1.4" }{TEXT -1 9 " below. " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 265 12 "Exercise 1.1" }}{PARA 0 "" 0 "" {TEXT 261 35 "Use Maple to calculate \+ the number " }{XPPEDIT 18 0 "37^43" "6#*$\"#P\"#V" }{TEXT 266 3 " . \+ " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 267 21 "Student Workspace 1.1" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 " " {TEXT 269 12 "Exercise 1.2" }}{PARA 0 "" 0 "" {TEXT 270 10 "Calculat e " }{XPPEDIT 18 0 "sqrt(34)" "6#-%%sqrtG6#\"#M" }{TEXT 282 16 " to 18 digits. " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 271 21 "Student Workspace 1.2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 273 12 "Exercise 1.3" }}{PARA 0 "" 0 "" {TEXT 274 54 "Find a numerical approximation for the expressio n : " }{XPPEDIT 18 0 "(3+Pi)/(7-sqrt(13))" "6#*&,&\"\"$\"\"\"%#PiGF& F&,&\"\"(F&-%%sqrtG6#\"#8!\"\"F." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 275 21 "Student Workspace 1.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 277 12 "Exercise 1.4" }}{PARA 0 "" 0 "" {TEXT -1 101 "The percent sign ( \+ %) is a handy shortcut but it can occasionally lead to some unexpecte d results. " }}{PARA 0 "" 0 "" {TEXT -1 20 "Here is an example. " }} {PARA 0 "" 0 "" {TEXT -1 96 "First execute each of the next three line s. You should be able to predict the result in advance." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "4+Pi;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "%+10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 46 "Now go back and re-e xecute the last line (i.e." }{MPLTEXT 1 0 5 "%+10;" }{TEXT -1 37 "). N ote that the output changes from " }{XPPMATH 20 "6#$\"+l#fTr\"!\")" } {TEXT -1 4 " to " }{XPPMATH 20 "6#$\"+l#fTr#!\")" }}{PARA 0 "" 0 "" {TEXT -1 20 "Can you explain why?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {SECT 1 {PARA 20 "" 0 "" {TEXT 278 21 "Student Workspace 1.4" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Clearing Variables" }}{PARA 0 "" 0 "" {TEXT -1 194 "Once you have defined a variable, Maple will remember it s value during your entire working session. If you want to overwrite \+ the variable with a new value, you can simply make a new assignment." }}{PARA 0 "" 0 "" {TEXT -1 160 "For example each assignment below rede fines the value of the variable h. (Note: to check the current value f or a variable just type it followed by a semicolon.)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "h;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "h:=56;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "h;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "h:=sqrt(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "h;" }}}{PARA 0 "" 0 "" {TEXT -1 100 "Sometimes you will want to \"clear\" a variable in memory so that you can use it in a new situation. " }}{PARA 0 "" 0 "" {TEXT -1 51 "Here is an example. First we assign x the value 65." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "x:=65;" }}}{PARA 0 "" 0 "" {TEXT -1 91 "Now ass ume that we start a new problem and want to enter the general algebrai c expression " }{XPPEDIT 18 0 "x^2-4*x+7" "6#,(*$%\"xG\"\"#\"\"\"*&\" \"%F'F%F'!\"\"\"\"(F'" }{TEXT -1 108 " and assign it the name w. If we just enter this, Maple automatically substitutes the previous value f or x. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "w:=x^2-4*x+7;" }}} {PARA 0 "" 0 "" {TEXT -1 208 "In order to get x to be a general variab le again we must first \"clear\" (i.e. erase from Maple's memory) our \+ earlier value for x. This is accomplished by entering x:='x'; Note t hat we use single quotes here." }}{PARA 0 "" 0 "" {TEXT -1 49 "Execute the next two lines to see how this works." }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 7 "x:='x';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "w:=x^2-4*x+7;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 303 36 "Clearing all variables at once: the " }{TEXT 302 7 "rest art" }{TEXT 304 10 " command. " }}{PARA 0 "" 0 "" {TEXT -1 4 "The " } {TEXT 300 7 "restart" }{TEXT -1 176 " command will clear Maple's memor y of all definitions that you have made. It is like starting a new Map le session. If you are starting a completely new problem you can use t he " }{TEXT 301 7 "restart" }{TEXT -1 155 " command to guarantee that \+ there are no leftover definitions from your earlier work. Before you \+ execute the second line below, quickly predict the output." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p:=4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "p; x; h;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "Y ou probably remembered that p was 4 and x had been reassigned to be th e variable x, but you may not have remembered that h was assigned the \+ value " }{XPPEDIT 18 0 "sqrt(Pi)" "6#-%%sqrtG6#%#PiG" }{TEXT -1 38 ". \+ That's why it's a good idea to use " }{TEXT 305 7 "restart" }{TEXT -1 127 " to remove all definitions at once. (As you work through this tutorial you will notice that we start most new sections with a " } {TEXT 306 7 "restart" }{TEXT -1 11 " command.) " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "p; x; h;" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }