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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "              " }}{PARA 0 
"" 0 "" {TEXT -1 134 "                                                \+
                                                                  Math
 23, Spring 2003" }}{PARA 0 "" 0 "" {TEXT -1 123 "                    \+
                                                                      \+
                        B. Dodson" }}{PARA 0 "" 0 "" {TEXT -1 130 "   \+
                                                                      \+
                                         Sections 110-313" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "                  \+
   Maple worksheet:  practice for Extra Credit and HW3 maple problems.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1+2;" }{TEXT -1 150 "           \+
                                                                      \+
                                                                     \+
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "3/23;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"$\"#B
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(3/23);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+EyM/8!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "sqrt(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG
6#\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(sqrt
(3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+330K<!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "# The top of this worksheet was ent
ered in \"text mode\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "# \+
This is \"maple input mode\";  in which comments are " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "# entered on lines starting with '#
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "The above illustra
te \"basic\" maple commands.  For further information on these and " }
}{PARA 0 "" 0 "" {TEXT -1 80 "the following, please see the \"maplebas
icsweb21\" file.  We continue by giving a " }}{PARA 0 "" 0 "" {TEXT 
-1 80 "Maple version of the solution to Problem 9, section 2.8 (which \+
closely resembles" }}{PARA 0 "" 0 "" {TEXT -1 50 "the Extra Credit pro
blem 10 of the same section). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "F:= x -> x^3-5*x+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGR
6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"$\"\"\"F1*&\"\"&F1F/F1!\"
\"F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?diff" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Fprime:= x -> diff(F(x),x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'FprimeGR6#%\"xG6\"6$%)operatorG
%&arrowGF(-%%diffG6$-%\"FG6#9$F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "subs(x=1,Fprime(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(F(x),x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"\"\"$\"\"&!\"\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "If one remembers that Maple h
as a command for differentiation, then" }}{PARA 0 "" 0 "" {TEXT -1 74 
"there is online help:  entering \"?diff\" brings up the help file.  A
s we've" }}{PARA 0 "" 0 "" {TEXT -1 70 "just checked, Fprime is the (M
aple function) that is the derivative of" }}{PARA 0 "" 0 "" {TEXT -1 
67 "F(x);  and -2 = 3*(1)^2 -5 is the value of the derivative at x = 1
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(x=1,F(x));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "# the point (1,-3) is the point on the graph" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "# with x = 1;  so the tangent line \+
given by" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "# y = F(1) + Fp
rime(1) * (x-1) is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "lin:= x -> -3+(-2)*(x-1);" }
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wGF(,&!\"\"\"\"\"*&\"\"#F.9$F.F-F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "# so a solution to part (b) of problem 9 should be" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot([F,lin]);" }}{PARA 
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0 "> " 0 "" {MPLTEXT 1 0 51 "# Not a Good solution!  Without instructi
on, \"plot\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "# takes x f
rom -10 to 10;  which in Maple is x=-10..10." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 42 "# We try again with a smaller plot window:" }}}
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