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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Clipper Calculus  Written As
signment 1\nDue (printed and postmarked) February 8" }}{PARA 0 "" 0 "
" {TEXT -1 7 "\nNAME:\n" }}{PARA 0 "" 0 "" {TEXT -1 116 "Save your wor
k often.  Insert text (press F5), input prompts (click on the prompt i
con [>),  and space as needed.\n \n" }{TEXT 256 55 "Execute the follow
ing before beginning this assignment:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "with(student):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Some usef
ul commands (see the MAPLE Demonstration 1 for examples)" }}{PARA 0 "
" 0 "" {TEXT -1 65 "f:=x->x^2                            create the fu
nction f(x)=x^2" }}{PARA 0 "" 0 "" {TEXT -1 62 "plot(f(x),x)          \+
                sketch the graph of f(x)" }}{PARA 0 "" 0 "" {TEXT -1 
74 "plot(f(x),x=a..b)                 sketch the graph of f(x)  for x \+
in [a,b]" }}{PARA 0 "" 0 "" {TEXT -1 84 "plot(f(x),x=a..b,y=c..d)    s
ketch the graph of y=f(x) for x in [a,b] and y in [c,d]" }}{PARA 0 "" 
0 "" {TEXT -1 85 "plot([f(x),g(x)],x)              sketch the graphs o
f f(x) and g(x) in the same plane" }}{PARA 0 "" 0 "" {TEXT -1 78 "plot
([f(x),g(x)],x=a..b)     sketch the graphs of f(x) and g(x) for x in [
a,b]" }}{PARA 0 "" 0 "" {TEXT -1 71 "solve(f(x)=0,x)                  \+
 symbolically solve the equation for x" }}{PARA 0 "" 0 "" {TEXT -1 91 
"fsolve(f(x)=0,x)                 numerically solve for x             \+
                      " }}{PARA 0 "" 0 "" {TEXT -1 67 "fsolve(f(x)=0,x
=a..b)        numerically solve for x in [a,b]      " }}{PARA 0 "" 0 "
" {TEXT -1 68 "evalf(expression)              numerically approximate \+
to ten digits" }}{PARA 0 "" 0 "" {TEXT -1 65 "evalf(expression,n)     \+
      numerically approximate to n digits" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 258 "" 0 "" {TEXT -1 65 "NOTE:  When writing decimals,  i
nclude a digit to the left of the" }}{PARA 258 "" 0 "" {TEXT -1 67 "de
cimal point.   In other words, write 0.5 not .5 for five tenths. " }}
{PARA 258 "" 0 "" {TEXT -1 30 "This will avoid some problems." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "P
roblem 1. Execute the following command to define the function f(x):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "f:=x->x*(((x-1)^2)^(1/3)*
(sin(1/(x-1)))+(0.1)*(x-1)+0.1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "a)  Use Maple to plot the  graph o
f f(x) (the command is given below)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(f(x),x=-3..4, y=-3..
3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 61 "b)  Now plot the graph over a small interval containing x=1. " 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 83 "c) Explain what the graph is showing you \+
near x=1; especially over a small interval" }}{PARA 0 "" 0 "" {TEXT 
-1 65 "(type your explanation below).  Why does it look the way it doe
s?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Problem 2.  \+
Execute the following command:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "f:=x->x^2 - 10;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Rememb
er from the Maple Basics worksheet that this defines a function f(x). \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "a)  \+
Use the solve( ) command to find the x-intercepts of the function  f(x
).  You need the (x) part." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 83 "b)  Use the fsolve( ) command to approximate the x
-intercepts of the function f(x)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Problem 3.  Execute the following \+
command:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=x->x^3 -x +1
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 269 "a)  Use the plot( ) command
 to produce an  S-shaped  graph of the function  g(x).  You will have \+
to determine a choice of interval,   x = a..b, which will give\na  goo
d picture of the function.  Be sure that your graph captures the inter
esting features of the function.\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 "b) Zoom in to find the coordinate
s of the point at which the graph changes direction from rising to fal
ling. Include the graph as well as the coordinates (approximately) of \+
the point." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 18 "End of assignment." }}}}{MARK "3 0 0" 56 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }