{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{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 "Title
" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }
3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" 
-1 -1 "Times" 1 14 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 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 28 "Arc length for a space cu
rve" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Example: (1) Plot the following s
pace curve from t =0 to t = 4*Pi. (2) Find the arc length of the space
 curve." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "x:=cos(t); y:=si
n(t); z:=t^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "spacecurve
([x,y,z],t=0..4*Pi,axes=BOXED);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "d1:=diff(x,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "d
2:=diff(y,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "d3:=diff(z
,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "h:=t->((d1)^2+(d2)^
2+(d3)^2)^(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(t);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L:=Int(((d1)^2+(d2)^2)^(1/
2),t=0..4*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Example: (a) Plot the followi
ng space curve and (2) find its arc length from t =0 to 4*Pi. " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "spacecurve([exp(-t)*cos(10*t
),exp(-t)*sin(10*t),exp(-t)],t=0..4*Pi,axes=BOXED,numpoints=500);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "x:=exp(-t)*cos(10*t); y:=exp
(-t)*sin(10*t); z:=exp(-t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "d1:=diff(x,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "d2:=d
iff(y,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "d3:=diff(z,t);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "h:=t->((d1)^2+(d2)^2+(d
3)^2)^(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L:=Int(((d1)^2+(d2)^2)^(1/2)
,t=0..4*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }
{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 5 }
{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }