{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 "" 0 1 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 "Title" 
0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 
12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{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 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 24 "Limit of the Riemann Sum
" }}{PARA 19 "" 0 "" {TEXT -1 12 "Wei-Chi Yang" }}{PARA 256 "" 0 "" 
{TEXT -1 23 "e-mail: wyang@runet.edu" }}{PARA 256 "" 0 "" {TEXT -1 32 
"URL: http://www.runet.edu/~wyang" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 74 "In this worksheet, we will use Maple to f
ind the limit of the Riemann sum." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "f:=x->tan(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "right:=proc(a,b,j,n) a+j*(b-a)/n end;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "left:=proc(a,b,j,n)  a+(j-1)*(b-a)/
n end;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "rsum:=proc(a,b,n) sum(((b-a)/n)*f(right(a,b,j,n)),j=1
..n) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "limit(rsum(0,P
i/4,n),n=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf
(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "lsum:=proc(a,b,n) s
um(((b-a)/n)*f(left(a,b,j,n)),j=1..n) end;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 33 "limit(lsum(0,Pi/4,n),n=infinity);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "midpoint:=proc(a,b,j,n) (left(a,b,j,n)+right(a,b,j,n)
)/2 end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "msum:=proc(a,b,
n) sum(((b-a)/n)*f(midpoint(a,b,j,n)),j=1..n) end;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 33 "limit(msum(0,Pi/4,n),n=infinity);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 41 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }