{VERSION 4 0 "IBM INTEL LINUX" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 
"" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 18 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "
" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "
" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 
0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 
{CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 
263 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 1 24 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "
" 0 265 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 266 1 {CSTYLE "" -1 -1 "" 1 
18 0 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 }
{PSTYLE "" 0 267 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 268 1 {CSTYLE "" -1 
-1 "" 1 18 0 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 }{PSTYLE "" 0 269 1 {CSTYLE "" -1 -1 "" 1 18 0 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 264 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" 
{TEXT 260 10 "Calculus I" }}{PARA 263 "" 0 "" {TEXT 261 15 "The Power \+
Rule:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 "" 
{TEXT -1 33 "In this lab we will use maple to " }}{PARA 265 "" 0 "" 
{TEXT -1 47 "compute derivatives for various powers of x.   " }}{PARA 
256 "" 0 "" {TEXT -1 25 "We begin by defining the " }{TEXT 256 22 "dif
ferential quotient " }{TEXT 263 3 "for" }{TEXT 264 1 " " }{XPPEDIT 18 
0 "x^2" "6#*$%\"xG\"\"#" }{MPLTEXT 0 21 1 "." }}{PARA 0 "" 0 "" {TEXT 
265 55 "We use the expand operation to simplify the expression." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dq := ((x+h)^2 - x
^2)/h;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dqs := expand(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h := 0;" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 14 "fprime := dqs;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 51 "We consider the same pro
blem for x^3.  Observe the " }}{PARA 266 "" 0 "" {TEXT -1 44 "pattern \+
and predict a pattern for any power " }{TEXT 267 2 "n." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "dq1 := ((x+h)^3 - x^3)/h;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dq
2 := expand(%);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h := 0;" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "fprime := dq2;" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 50 "Now compute the derivat
ives using this method for " }{XPPEDIT 18 0 "x^4,x^5,x^6,x^22" "6&*$%
\"xG\"\"%*$F$\"\"&*$F$\"\"'*$F$\"#A" }{TEXT -1 1 "." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" 
{TEXT -1 57 "Finally, compute the derivatives for all the cases above \+
" }}{PARA 267 "" 0 "" {TEXT -1 27 "using the following method:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 27 "dq1 := (x^2 - a^2)/(x - a);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "dq2 := simplify(%);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 7 "x := a;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "fprim
e := dq2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 268 "" 0 "
" {TEXT -1 73 "Discuss briefly the differences and similarities betwee
n the two methods." }}{PARA 269 "" 0 "" {TEXT -1 35 "Which method do y
ou prefer and why?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}}{MARK "0 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }