{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 }{CSTYLE "2D Math" -1 2 "Times" 0 0 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 "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "mmm" -1 259 "" 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 270 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 272 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } {CSTYLE "" 18 275 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 279 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 283 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } {CSTYLE "" 18 285 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 288 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 290 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 291 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 293 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 297 "" 1 14 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 1 14 0 0 0 0 0 2 0 0 0 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 259 "" 0 "" {TEXT 278 11 "Riemann Sum" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 26 "Here are the sums commands" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "leftsum(x^2,x=0..30,10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "rightsum(x^2,x=0..30,10):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 9 "evalf(%):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Th e commands" }{TEXT 19 1 " " }{TEXT 267 7 "leftbox" }{TEXT -1 3 ", " } {TEXT 268 8 "rightbox" }{TEXT -1 6 ", and " }{TEXT 269 9 "middlebox" } {TEXT -1 63 " will draw the curve with any number of rectangles, as fo llows." }{TEXT 19 0 "" }{TEXT 18 0 "" }{TEXT 19 0 "" }{TEXT -1 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "leftbox(x^2,x=0..30,10,shad ing=cyan):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "rightbox(x^2, x=0..30,10,shading=aquamarine):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "middlebox(x^2,x=0..30,10,color=blue,shading=yellow):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 0 "" 0 " " {TEXT 273 13 "Exercise 1: " }{TEXT 270 12 "Use Maple's " }{TEXT 272 3 "sum" }{TEXT 271 71 " function to create and evaluate the left-h and and right-hand sums for " }}{PARA 0 "" 0 "" {TEXT 297 30 "n = 10 s ubintervals. Use the " }{TEXT 276 7 "leftsum" }{TEXT 277 4 " and" } {TEXT 279 1 " " }{TEXT 275 8 "rightsum" }{TEXT 274 33 " commands to co nfirm your answers" }{TEXT 280 2 ". " }{TEXT -1 1 " " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 18 0 "f(x) = 4-x^2;" "6#/-%\"fG6#%\"xG,&\"\"%\"\"\"*$F'\"\"#!\"\"" } {TEXT -1 12 " , 0 < x < 2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 20 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Exercise 2: " }{TEXT 281 12 "Use Maple's " } {TEXT 283 3 "sum" }{TEXT 282 71 " function to create and evaluate the \+ left-hand and right-hand sums for " }}{PARA 3 "" 0 "" {TEXT 298 30 "n \+ = 20 subintervals. Use the " }{TEXT 286 7 "leftsum" }{TEXT 287 4 " an d" }{TEXT 288 1 " " }{TEXT 285 8 "rightsum" }{TEXT 284 33 " commands t o confirm your answers" }{TEXT 289 2 ". " }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "f(x) = exp(x);" "6#/-%\"fG6#%\"xG-%$expG6#F'" }{TEXT -1 12 " , 1 < x < 4" }}{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 "" {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 "" }}}{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 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Exercise 3: " }{TEXT 290 91 "Use left-hand and right-hand sums with 15 subintervals to approximate the area bounded \+ by " }{XPPEDIT 291 0 "y = sin(x);" "6#/%\"yG-%$sinG6#%\"xG" }{TEXT -1 1 " " }{TEXT 292 33 "and the x-axis between x = 0 and " }{XPPEDIT 293 0 "x = Pi/4;" "6#/%\"xG*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT 294 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 "" {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 " " }}}{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 "" }}}}}{MARK "2 7 0 11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }