{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "#Make Maple Lie" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#Maple knows the quadratic f
ormula" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(a*x^2+b*x+c
=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#Maple knows the \+
cubic formula" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(a*x^
3+b*x^2+c*x+d=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#Map
le knows 4th degree equations " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "solve(a*x^4+b*x^3+c*x^2+d*x+e=0,x);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 91 "#The RootOf notation doesn't look like much gain, \+
but then the allvalues command tells more" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 46 "allvalues(solve(a*x^4+b*x^3+c*x^2+d*x+e=0,x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "# 5th degree equations are i
mpossible to solve in general" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 41 "solve(a*x^5+b*x^4+c*x^3+d*x^2+e*x+f=0,x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 52 "allvalues(solve(a*x^5+b*x^4+c*x^3+d*x^2+e*x+f=
0,x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# particular 5th \+
degree equations can be solved" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "quintic:=x^5-x^3-1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "solve(quintic);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "allv
alues(solve(quintic));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "
# Note that maple includes the complex roots, 4 of the 5 roots are com
plex. Often plotting the function gives a better idea (but it takes a \+
while to find the correct ranges.)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "plot(quintic,x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 151 "# Armed with this information, one can use th
e numerical method fsolve(exp,var,range) to find a numerical approx to
 the root of exp in the range range." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "fsolve(quintic=0,x,1..2);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 57 "# Checking ranges without roots get the silent trea
tment " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(quintic=0,
x,-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "# another meth
od for finding numerical answers is with evalf, (but we lose stuff)" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf(solve(quintic,x));" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#Problem 1 f(x)=x^3-6*x+1
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "#a. Show f has 3 real \+
roots by plotting the function and using fsolve to approx each" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "#b. Explain why evalf(solve
(f(x)=0,x)) cannot be the roots of a cubic equation (with integer coef
ficients) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#c. Why did M
aple make this error?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "#P
roblem 2 f(x)=exp(x)+sin(x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
97 "#a Show f has infinitely many roots by plotting (well show enough \+
of the plot to see the pattern)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "#b How many roots does maple find? " }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 57 "#c Use fsolve to find the 3 largest roots of e^x+s
in(x)=0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#Problem 3 f(x)=
sin(x)-cos(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "#a Plot \+
both sin and cos for 0..2*Pi, by inspection write down the infinite fa
mily of solutions to the roots of f. " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "#b How many roots does Maple find to f(x)=0?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "#c There is a Maple variable
 _EnvAllSolutions, get maple to give your answer to a." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "old:=_EnvAllSolutions;solve(sin(x)=
0);_EnvAllSolutions:=true;solve(sin(x)=0);_EnvAllSolutions:=old;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#Problem 4 Prove 2+2=5 with \+
Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "# define a to be \+
2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "# add a+a;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "# define a to be 5/2 [on a s
eparate line after the a+a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
45 "# go back and execute the old a+a line again." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 36 "# erase the line which makes a = 2.5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "#Problem 5 For the given f,
 find both x and y ranges which \"show\" all the features of the funct
ion f \"nicely\". Features include zeros of f, f' and f'' and hence al
l local extrema and points of inflection." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "#a f=xe^(-x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "#b f=x^2*exp(x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{MARK "46 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }