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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Quiz 7 MCS 320 Friday 7 Ma
rch 2003" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "1.  Give the Maple
 command to compute a third order Taylor series of tan(x) at x = 1." }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "     Give th
e first three decimal places of a floating-point approximation of this
 series at x = 1.1." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" 
{TEXT -1 8 "ANSWER :" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "ts := taylor(tan(x),x=1,3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#tsG++,&%\"xG\"\"\"F(!\"\"-%$tanG6#F(\"\"!,&F(F(*$)F*
\"\"#F(F(F(*&F*F(F.F(F1-%\"OGF,\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "order(ts);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "evalf(subs(x=1.1,convert(
ts,polynom)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-*3L&>!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "%-tan(1.1);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$!)b2X6!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
57 "Up to a factor, the Legendre polynomial can be defined by" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "             \+
                                    k" }}{PARA 0 "" 0 "" {TEXT -1 74 "
                              k!             d             2          \+
   k" }}{PARA 0 "" 0 "" {TEXT -1 61 "          p  (x)   = ---------   \+
 --------   (  x     -   1 )" }}{PARA 0 "" 0 "" {TEXT -1 46 "         \+
   k              (2k)!             k" }}{PARA 0 "" 0 "" {TEXT -1 48 "
                                              dx" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 150 "Give the Maple command to define the function p(k
,x) which takes on input the degree k and the variable x.  On return i
s the polynomial defined above." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 117 "Compare the result of p(5,x) with the result of \+
orthopoly[P](5,x).  What is the factor of difference between the two?
" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 7 "ANSWER:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "p := (k
,x) -> (k!/((2*k)!))*diff((x^2-1)^k,x$k);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"pGf*6$%\"kG%\"xG6\"6$%)operatorG%&arrowGF)*(-%*fact
orialG6#9$\"\"\"-F/6#,$F1\"\"#!\"\"-%%diffG6$),&*$)9%F6F2F2F2F7F1-%\"$
G6$F?F1F2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p5 := ex
pand(p(5,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p5G,(*$)%\"xG\"\"&
\"\"\"F**&#\"#5\"\"*F**$)F(\"\"$F*F*!\"\"*&#F)\"#@F*F(F*F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "l5 := orthopoly[P](5,x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#l5G,(*$)%\"xG\"\"&\"\"\"#\"#j\"\")*&#\"#N
\"\"%F**$)F(\"\"$F*F*!\"\"*&#\"#:F-F*F(F*F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 17 "coeff(l5,x,5)*p5;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,(*$)%\"xG\"\"&\"\"\"#\"#j\"\")*&#\"#N\"\"%F(*$)F&\"\"$F(F(!\"\"*&#
\"#:F+F(F&F(F(" }}}}{MARK "2 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 
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