{VERSION 4 0 "APPLE_PPC_MAC" "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 "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" 
-1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 
1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 
"Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 
}{PSTYLE "" 256 258 1 {CSTYLE "" -1 -1 "" 0 1 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 }}
{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 0 "" }{TEXT 256 24 "Euler's \+
Method Worksheet" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 4 "Name" }{TEXT -1 
10 ":         " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 
0 "" {TEXT -1 12 "Introduction" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "1) What does Y'(t) represent?" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "2) What are the units of Y'(t)?" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 257 "" 0 "" {TEXT -1 14 "Euler's Method" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "3) Caculate Y'(
0), that is, what is the slope of the line tangent to the function Y a
t 0?" }}{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 26 "4) Use Y'(0) to calculate " }
{XPPEDIT 18 0 "Delta y[1]" "6#*&%&DeltaG\"\"\"&%\"yG6#F%F%" }{TEXT -1 
2 ". " }}{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 7 "5) Use " }{XPPEDIT 18 0 "Delta y[1]
" "6#*&%&DeltaG\"\"\"&%\"yG6#F%F%" }{TEXT -1 14 " to calculate " }
{XPPEDIT 18 0 "y[1]" "6#&%\"yG6#\"\"\"" }{TEXT -1 1 "." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "6) What is th
e first estimate of Y at t = .5?" }}{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 19 "7) Is the v
alue of " }{XPPEDIT 18 0 "y[1]" "6#&%\"yG6#\"\"\"" }{TEXT -1 69 " an u
nderestimate or an over estimate of the the function Y at t =.5?" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "8) Find an expression for the erro
r in terms of Y and " }{XPPEDIT 18 0 "y[1]" "6#&%\"yG6#\"\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 0 "" }{TEXT -1 36 "9) Calcula
te the rate of change, Y'(" }{XPPEDIT 18 0 "t[1]" "6#&%\"tG6#\"\"\"" }
{TEXT -1 3 "). " }}{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 47 "10) Use your answer to questi
on 9 to calculate " }{XPPEDIT 18 0 "Delta y[2]" "6#*&%&DeltaG\"\"\"&%
\"yG6#\"\"#F%" }{TEXT -1 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 48 "11) Using y
our answer to question 10, calculate " }{XPPEDIT 18 0 "y[2]" "6#&%\"yG
6#\"\"#" }{TEXT -1 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 57 "12) State the
 coordinates of this second estimated point." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "13) Is the value of " }
{XPPEDIT 18 0 "y[2]" "6#&%\"yG6#\"\"#" }{TEXT -1 51 " an underestimate
 or an overestimate of Y at t = 1?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{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 0 "" }{TEXT 
258 15 "Table of Values" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 54 "14) Complete the table of values and sket
ch the graph:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 17 "   Point #       " }{XPPEDIT 18 0 "t[n]" "6#&%\"tG6#%\"nG
" }{TEXT -1 14 "              " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG
" }{TEXT -1 14 "           Y'(" }{XPPEDIT 18 0 "t[n]" "6#&%\"tG6#%\"nG
" }{TEXT -1 9 ")        " }{XPPEDIT 18 0 "Delta t" "6#*&%&DeltaG\"\"\"
%\"tGF%" }{TEXT -1 6 "      " }{XPPEDIT 18 0 "Delta y[n+1]" "6#*&%&Del
taG\"\"\"&%\"yG6#,&%\"nGF%F%F%F%" }{TEXT -1 6 "      " }{XPPEDIT 18 0 
"y[n+1] " "6#&%\"yG6#,&%\"nG\"\"\"F(F(" }{TEXT -1 25 "                \+
         " }}}{EXCHG {PARA 0 "" 0 "" {SPREADSHEET {NAME "SpreadSheet00
2" } {ROWHEIGHTS 1 36 2 36 3 36 4 36 5 36 6 36 } {COLWIDTHS 2 81 3 81 
5 67 6 67 7 94 } {SSOPTS {CELLOPTS 2 10 4 2 1 255 255 255 }0 }384 178 
178 {CELL 1 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "0" 20 "6#\"\"!
" }0 }{CELL 1 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "0" 20 "6#\"\"
!" }0 }{CELL 1 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "1" 20 "6#\"
\"\"" }0 }{CELL 1 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "1" 20 "6#
\"\"\"" }0 }{CELL 1 5 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ ".5" 20 
"6#$\"\"&!\"\"" }0 }{CELL 1 6 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ 
".5" 20 "6#$\"\"&!\"\"" }0 }{CELL 1 7 {CELLOPTS 0 -1 -1 0 0 0 0 0 }
{R5MATHOBJ "1.5" 20 "6#$\"#:!\"\"" }0 }{CELL 2 1 {CELLOPTS 0 -1 -1 0 
0 0 0 0 }{R5MATHOBJ "1" 20 "6#\"\"\"" }0 }{CELL 2 2 {CELLOPTS 0 -1 -1 
0 0 0 0 0 }{R5MATHOBJ ".5" 20 "6#$\"\"&!\"\"" }0 }{CELL 2 3 {CELLOPTS 
0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "1.5" 20 "6#$\"#:!\"\"" }0 }{CELL 2 4 
{CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2" 20 "6#\"\"#" }0 }{CELL 2 
5 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ ".5" 20 "6#$\"\"&!\"\"" }0 }
{CELL 2 6 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "1" 20 "6#\"\"\"" }
0 }{CELL 2 7 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2.5" 20 "6#$\"#D
!\"\"" }0 }{CELL 3 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2" 20 "6
#\"\"#" }0 }{CELL 3 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "1" 20 "
6#\"\"\"" }0 }{CELL 3 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2.5" 
20 "6#$\"#D!\"\"" }0 }{CELL 3 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }
{R5MATHOBJ "3" 20 "6#\"\"$" }0 }{CELL 3 5 {CELLOPTS 0 -1 -1 0 0 0 0 0 
}{R5MATHOBJ ".5" 20 "6#$\"\"&!\"\"" }0 }{CELL 4 1 {CELLOPTS 0 -1 -1 0 
0 0 0 0 }{R5MATHOBJ "3" 20 "6#\"\"$" }0 }{CELL 4 2 {CELLOPTS 0 -1 -1 
0 0 0 0 0 }{R5MATHOBJ "1.5" 20 "6#$\"#:!\"\"" }0 }{CELL 5 1 {CELLOPTS 
0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "4" 20 "6#\"\"%" }0 }{CELL 5 2 
{CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2" 20 "6#\"\"#" }0 }{CELL 6 
1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "5" 20 "6#\"\"&" }0 }{CELL 
6 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "2.5" 20 "6#$\"#D!\"\"" }
0 }{CELL 6 7 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "11.5" 20 "6#$\"$
:\"!\"\"" }0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots)
:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "Enter the numbers from your \+
table in the Maple command below, and graph your Euler approximation. \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 50 "eulerpoints1:=[[?,?],[?,?],[?,?],[?,?][?,?][?,
?]];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "graph1:=plot(eulerp
oints1,t=0..3,y=0..12,color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "display(graph1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "15) Assuming \+
that you know the values for point 20, find the values for point 21." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {SPREADSHEET {NAME "SpreadSheet001
" } {ROWHEIGHTS 1 36 2 36 } {COLWIDTHS 5 67 6 94 } {SSOPTS {CELLOPTS 
2 10 4 2 1 255 255 255 }0 }343 76 76 {CELL 1 1 {CELLOPTS 0 -1 -1 0 0 
0 0 0 }{R5MATHOBJ "20" 20 "6#\"#?" }0 }{CELL 1 2 {CELLOPTS 0 -1 -1 0 
0 0 0 0 }{R5MATHOBJ "10" 20 "6#\"#5" }0 }{CELL 1 3 {CELLOPTS 0 -1 -1 
0 0 0 0 0 }{R5MATHOBJ "106" 20 "6#\"$1\"" }0 }{CELL 1 4 {CELLOPTS 0 
-1 -1 0 0 0 0 0 }{R5MATHOBJ "21" 20 "6#\"#@" }0 }{CELL 1 5 {CELLOPTS 
0 -1 -1 0 0 0 0 0 }{R5MATHOBJ ".5" 20 "6#$\"\"&!\"\"" }0 }{CELL 1 6 
{CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "10.5" 20 "6#$\"$0\"!\"\"" }0 
}{CELL 1 7 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "116.5" 20 "6\"" }
0 }{CELL 2 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "21" 20 "6#\"#@" 
}0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "16) W
rite the expressions for " }{XPPEDIT 18 0 "Delta y[k+1]" "6#*&%&DeltaG
\"\"\"&%\"yG6#,&%\"kGF%F%F%F%" }{TEXT -1 7 " , and " }{XPPEDIT 18 0 "y
[k+1]" "6#&%\"yG6#,&%\"kG\"\"\"F(F(" }{TEXT -1 1 "." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {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 58 "17) Given the
 rate of change Y'(t) and the initial point (" }{XPPEDIT 18 0 "t[0]" "
6#&%\"tG6#\"\"!" }{TEXT -1 1 "," }{XPPEDIT 18 0 "y[0]" "6#&%\"yG6#\"\"
!" }{TEXT -1 121 "), explain, in your own words, how the following for
mulas can be used to calculate coordinates for the successive points.
" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "t[k+1]=t[k]+Delta t" "6#/&%\"tG6#
,&%\"kG\"\"\"F)F),&&F%6#F(F)*&%&DeltaGF)F%F)F)" }}{PARA 256 "" 0 "" 
{XPPEDIT 18 0 "y[k+1]" "6#&%\"yG6#,&%\"kG\"\"\"F(F(" }{TEXT -1 1 "=" }
{XPPEDIT 18 0 "y[k]" "6#&%\"yG6#%\"kG" }{TEXT -1 4 "+Y'(" }{XPPEDIT 
18 0 "t[k]" "6#&%\"tG6#%\"kG" }{TEXT -1 2 ") " }{XPPEDIT 18 0 "Delta t
" "6#*&%&DeltaG\"\"\"%\"tGF%" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {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 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 10 "18) Using " }{XPPEDIT 18 0 "Delta t" "6#*&%&DeltaG
\"\"\"%\"tGF%" }{TEXT -1 116 " = .25, approximate Y(t) over the interv
al [0, 3] and plot the results on the same graph as you used in questi
on 14." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {SPREADSHEET {NAME "SpreadSheet003" 
} {ROWHEIGHTS } {COLWIDTHS } {SSOPTS {CELLOPTS 2 10 4 2 1 255 255 255 
}0 }326 218 218 }}}{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 29 "euler
points2=[[?,?]...[?,?]];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "graph2:=plot(???...);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 23 "display(graph1,graph2);" }}}{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 41 "19) Make a conjecture about how reducing " }{XPPEDIT 
18 0 "Delta t" "6#*&%&DeltaG\"\"\"%\"tGF%" }{TEXT -1 31 " will affect \+
the approximation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "20) Find a func
tion Y whose derivative is 2t + 1, and also satisfies Y(0)=1." }}
{PARA 0 "" 0 "" {TEXT -1 15 "Enter it below." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Y:=???;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "graph3:=plot(Y,t=0..3,y=0..1
2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 101 "21) Use the graph, and  your answer to question 2
0 to explain the role of the size of the intervals (" }{XPPEDIT 18 0 "
Delta t" "6#*&%&DeltaG\"\"\"%\"tGF%" }{TEXT -1 40 ") has on the error \+
of the approximation." }}{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 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "56 0 2" 4 }{VIEWOPTS 1 1 0 3 2 
1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }