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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT 256 17 "Practice Problems" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem No. 1" }}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 33 "Assign the name w to the number  " }{XPPEDIT 18 0 
"2*Pi/3" "6#*(\"\"#\"\"\"%#PiGF%\"\"$!\"\"" }{TEXT -1 20 "  and then f
ind the " }{TEXT 273 11 "exact value" }{TEXT -1 7 " and a " }{TEXT 
274 21 "decimal approximation" }{TEXT -1 20 " for the following: " }
{XPPEDIT 18 0 "w^2, sqrt(w)" "6$*$%\"wG\"\"#-%%sqrtG6#F$" }{TEXT -1 5 
" and " }{XPPEDIT 18 0 "cos(w)" "6#-%$cosG6#%\"wG" }{TEXT -1 3 " . " }
}}{SECT 1 {PARA 20 "" 0 "" {TEXT 258 18 "Student Workspace " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem \+
No. 2" }}{PARA 0 "" 0 "" {TEXT -1 9 "Factor   " }{XPPEDIT 18 0 "x^8-2*
x^4+1" "6#,(*$%\"xG\"\")\"\"\"*&\"\"#F'*$F%\"\"%F'!\"\"F'F'" }{TEXT 
-1 2 " ." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 259 18 "Student Workspace \+
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem \+
No. 3" }}{PARA 0 "" 0 "" {TEXT -1 19 "Enter the function " }{XPPEDIT 
18 0 "f(x)=20*x+30*x^2-sqrt(46-x^2)" "6#/-%\"fG6#%\"xG,(*&\"#?\"\"\"F'
F+F+*&\"#IF+*$F'\"\"#F+F+-%%sqrtG6#,&\"#YF+*$F'F/!\"\"F6" }{TEXT -1 1 
" " }}{PARA 0 "" 0 "" {TEXT -1 36 "Then find the approximate value of \+
 " }{XPPEDIT 18 0 "f(3.29) + f(-3.1) " "6#,&-%\"fG6#$\"$H$!\"#\"\"\"-F
%6#,$$\"#J!\"\"F0F*" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 267 18 "Student \+
Workspace " }}{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 "" {MPLTEXT 1 0 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 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 13 "Problem No. 4" }}{PARA 0 "" 0 "" {TEXT -1 50 "Find the \+
approximate value of  T in the formula   " }{XPPEDIT 18 0 "T = sqrt((2
*a-3*b^2)/(c-20))" "6#/%\"TG-%%sqrtG6#*&,&*&\"\"#\"\"\"%\"aGF,F,*&\"\"
$F,*$%\"bGF+F,!\"\"F,,&%\"cGF,\"#?F2F2" }{TEXT -1 1 " " }}{PARA 0 "" 
0 "" {TEXT -1 34 "when a=4.6  ,  b= -3.8  and c=2.9 " }}{SECT 1 {PARA 
20 "" 0 "" {TEXT 268 18 "Student Workspace " }}{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 "
" {MPLTEXT 1 0 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 "" {MPLTEXT 1 0 0 "" }}}}
}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem No. 5" }}{PARA 0 "" 0 "
" {TEXT -1 4 "If  " }{XPPEDIT 18 0 "f(x)=x^2-2*x+3" "6#/-%\"fG6#%\"xG,
(*$F'\"\"#\"\"\"*&F*F+F'F+!\"\"\"\"$F+" }{TEXT -1 26 " ,  find and sim
plify ,   " }{XPPEDIT 18 0 "f(3*t+2)" "6#-%\"fG6#,&*&\"\"$\"\"\"%\"tGF
)F)\"\"#F)" }{TEXT -1 3 " . " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 260 18 
"Student Workspace " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 13 "Problem No. 6" }}{PARA 0 "" 0 "" {TEXT -1 37 "When mult
iplied out the expression   " }{XPPEDIT 18 0 "(x-4)^2*(x+1)^3" "6#*&,&
%\"xG\"\"\"\"\"%!\"\"\"\"#,&F%F&F&F&\"\"$" }{TEXT -1 36 "  equals a fi
fth-degree polynomial. " }}{PARA 0 "" 0 "" {TEXT -1 32 "What is the co
efficient of the  " }{XPPEDIT 18 0 "x^2" "6#*$%\"xG\"\"#" }{TEXT -1 8 
"  term ?" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 269 18 "Student Workspace \+
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem \+
No. 7" }}{PARA 0 "" 0 "" {TEXT -1 22 "Plot the expressions  " }
{XPPEDIT 18 0 "cos(x) " "6#-%$cosG6#%\"xG" }{TEXT -1 6 " and  " }
{XPPEDIT 18 0 "cos(x)*sin(10*x)" "6#*&-%$cosG6#%\"xG\"\"\"-%$sinG6#*&
\"#5F(F'F(F(" }{TEXT -1 17 " on the interval " }{XPPEDIT 18 0 "[0,2*Pi
]" "6#7$\"\"!*&\"\"#\"\"\"%#PiGF'" }{TEXT -1 52 " . Then plot these sa
me expressions on the interval " }{XPPEDIT 18 0 "[0,4*Pi]" "6#7$\"\"!*
&\"\"%\"\"\"%#PiGF'" }{TEXT -1 1 "." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 
261 18 "Student Workspace " }}{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 "" {MPLTEXT 1 0 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 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 13 "Problem No. 8" }}{PARA 0 "" 0 "" {TEXT -1 20 "Plot
 the function   " }{XPPEDIT 18 0 "f(x)=sec(x) +4" "6#/-%\"fG6#%\"xG,&-
%$secG6#F'\"\"\"\"\"%F," }{TEXT -1 17 " on the interval " }{XPPEDIT 
18 0 "[0,2*Pi]" "6#7$\"\"!*&\"\"#\"\"\"%#PiGF'" }{TEXT -1 132 " . Auto
matic scaling does not produce a useful picture. Specify a y-range tha
t gives a good view of this function on this interval. " }}{SECT 1 
{PARA 20 "" 0 "" {TEXT 272 18 "Student Workspace " }}{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 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Problem No. 9" }}{PARA 0 "
" 0 "" {TEXT -1 17 "Recall that if a " }{TEXT 257 15 "rational number
" }{TEXT -1 151 " has an infinite decimal expansion then somewhere in \+
the expansion the digits must repeat. A familiar example is the decima
l expansion of the fraction " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$\"\"$!
\"\"" }{TEXT -1 103 " = .33333... where we have the digit 3 repeated. \+
 A bit more interesting is the decimal expansion for  " }{XPPEDIT 18 
0 "33/14" "6#*&\"#L\"\"\"\"#9!\"\"" }{TEXT -1 105 " = 2.3571428571428.
.. with the repeating digits 571428. Now look at a decimal expansion o
f the fraction  " }{XPPEDIT 18 0 "2/19" "6#*&\"\"#\"\"\"\"#>!\"\"" }
{TEXT -1 102 ". Can you identify the repeating sequence. Check yoursel
f by looking at one thousand decimal places.  " }}{SECT 1 {PARA 20 "" 
0 "" {TEXT 262 18 "Student Workspace " }}{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 "
" {MPLTEXT 1 0 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 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Problem \+
No. 10" }}{PARA 0 "" 0 "" {TEXT -1 41 "a) Plot the following points on
 a graph: " }}{PARA 0 "" 0 "" {TEXT -1 66 "( 1, 0.53) , (1.5, 0.65) , \+
(2, 0.91) , (2.5 , 0.95) and (3, 1.10 )" }}{PARA 0 "" 0 "" {TEXT -1 
53 "b) Create a single picture that has the points above " }{TEXT 264 
4 "plus" }{TEXT -1 27 " graphs of the functions : " }{XPPEDIT 18 0 "f(
x)=sin(x/2)" "6#/-%\"fG6#%\"xG-%$sinG6#*&F'\"\"\"\"\"#!\"\"" }{TEXT 
-1 6 " and  " }{XPPEDIT 18 0 "g(x)=x^2/5" "6#/-%\"gG6#%\"xG*&F'\"\"#\"
\"&!\"\"" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 95 "Use your pic
ture to decide which of these two functions most closely fits this set
 of points ? " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 263 18 "Student Worksp
ace " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 14 "Problem No. 11" }}{PARA 0 "" 0 "" {TEXT -1 49 "App
roximate all real solutions of the equation   " }{XPPEDIT 18 0 "x^4-4*
x^3+3*x-12=0" "6#/,**$%\"xG\"\"%\"\"\"*&F'F(*$F&\"\"$F(!\"\"*&F+F(F&F(
F(\"#7F,\"\"!" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{SECT 1 {PARA 20 "" 0 "" {TEXT 265 18 "Student Workspace " }}{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 "" {MPLTEXT 1 0 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 "" }}}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 14 "Problem No. 12" }}{PARA 0 "" 0 "" {TEXT -1 49 "Approxim
ate all real solutions of the equation   " }{XPPEDIT 18 0 "x^4-4*x^3=c
os(3*x)+3" "6#/,&*$%\"xG\"\"%\"\"\"*&F'F(*$F&\"\"$F(!\"\",&-%$cosG6#*&
F+F(F&F(F(F+F(" }{TEXT -1 2 " ." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 266 
18 "Student Workspace " }}{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 "" {MPLTEXT 1 0 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 "" }}}}
}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Problem No. 13" }}{PARA 0 "" 0 "
" {TEXT -1 16 "The graphs of   " }{XPPEDIT 18 0 "f(x)=20-x" "6#/-%\"fG
6#%\"xG,&\"#?\"\"\"F'!\"\"" }{TEXT -1 8 "  and   " }{XPPEDIT 18 0 "h(x
)=1.012^x" "6#/-%\"hG6#%\"xG)$\"%75!\"$F'" }{TEXT -1 26 "  intersect a
t one point. " }}{PARA 0 "" 0 "" {TEXT -1 107 "Use the numerical solvi
ng capabilities of Maple to approximate the coordinates of this inters
ection point. " }}{PARA 0 "" 0 "" {TEXT -1 51 "Start by entering an ap
propriate equation to solve." }}{PARA 0 "" 0 "" {TEXT -1 77 "Check you
r answer by creating a picture that shows the graphs intersecting.  " 
}}{SECT 1 {PARA 20 "" 0 "" {TEXT 270 18 "Student Workspace " }}{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 "" {MPLTEXT 1 0 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 "" }}}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 14 "Problem No. 14" }}{PARA 0 "" 0 "" {TEXT -1 31 "Solve fo
r r in the equation :  " }{XPPEDIT 18 0 "r*(p*k-18*m)=32*(2-p*r*m)/m^2
" "6#/*&%\"rG\"\"\",&*&%\"pGF&%\"kGF&F&*&\"#=F&%\"mGF&!\"\"F&*(\"#KF&,
&\"\"#F&*(F)F&F%F&F-F&F.F&*$F-F2F." }{TEXT -1 106 "  . Be sure that yo
u have entered the equation correctly. In particular check that you ha
ve used an * for " }{TEXT 275 5 "every" }{TEXT -1 16 " mulitplication.
" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 271 18 "Student Workspace " }}
{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 "" {MPLTEXT 1 0 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 "" }}}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0
" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }