{VERSION 4 0 "IBM INTEL NT" "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 12 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 12 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 259 29 "MATH-1850 COMPUTER PROBL EM 3" }{TEXT -1 54 " DUE: Tuesday, September 19, 2000, in your lab c lass" }}{PARA 0 "" 0 "" {TEXT -1 17 "\nTeam members: " }{TEXT 266 54 "(All lines for answers below will extend as you type.)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " \+ (1) " }{TEXT 263 17 " SOLUTION " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (2) " }{TEXT 264 9 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (3) " }{TEXT 262 0 "" }{TEXT -1 0 "" }{TEXT 265 9 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Score: / 6\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 257 13 "INSTRUCTIONS " }{TEXT 256 20 "(Click box in front)" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1254 " It is strongly suggested that this project be worked in teams (of up t o 3 persons). Approaches may be discussed among different teams, but \+ each team must write their OWN report.\nREQUIREMENTS OF REPORT:\n- Mat hematical contents (correctness and completeness) counts most. Solve t he problems and show all essential calculations (commands and output) \+ and plots. Please do not submit work that is not essential (e.g. check ing out how the function fplot in Problem 1 works - this may be essent ial to your understanding, but it s not essential for the reader).\n- \+ Explain the steps you carry out. Explain the approaches/techniques tha t you use.\n- Add explanations and answer questions where asked to do \+ so. By all means, include additional explanations/observations/conclus ions that come to your mind! (This could translate to extra credit.)\n HOW TO SUBMIT THE REPORT\nEach team submits ONE printed copy (stapled) by the due date. (Please save the electronic version, as you will be \+ asked to submit that, too, at a future time.)\nYou can print from insi de your Maple worksheet (choose File/Print or click on the printer but ton). Set the ZOOM FACTOR to 100% (smallest magnifying glass) before p rinting.\nPlease remove these instructions before submitting the repor t." }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Digits := 50:" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "1. Find " } {XPPEDIT 18 0 "Limit((10*x^3+47*x^2+54*x+9)/(6*x^3-x^2-42*x+45),x = -3 );" "6#-%&LimitG6$*&,**&\"#5\"\"\"*$%\"xG\"\"$F*F**&\"#ZF**$F,\"\"#F*F **&\"#aF*F,F*F*\"\"*F*F*,**&\"\"'F**$F,F-F*F**$F,F1!\"\"*&\"#UF*F,F*F: \"#XF*F:/F,,$F-F:" }{TEXT -1 25 " by doing the following:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 29 " (a) Write the expression " }{XPPEDIT 18 0 "(10*x^3+47*x^2+54*x+9)/(6*x^3-x^2-42*x+45);" "6#*&,**&\"#5\"\"\" *$%\"xG\"\"$F'F'*&\"#ZF'*$F)\"\"#F'F'*&\"#aF'F)F'F'\"\"*F'F',**&\"\"'F '*$F)F*F'F'*$F)F.!\"\"*&\"#UF'F)F'F7\"#XF'F7" }{TEXT -1 39 " as a fun ction f using Maple syntax. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "f := x -> (10*x^3+47*x^2+54*x+9)/(6*x^3-x^2-42*x+45);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 " \+ (b) Look at the values of f(" }{TEXT 267 1 "x" }{TEXT -1 5 ") as " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 53 " approaches - 3 from values that are larger than - 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "f(-2.999); f(-2.999999); f(-2.999999999); f(-2.999999999999); f(-2 .999999999999999);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 280 23 "Note: Other values of " }{TEXT 281 1 "x" }{TEXT 282 41 " are possible; just so that the value of " } {TEXT 283 1 "x" }{TEXT 284 31 " approaches - 3 from the right." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 " \+ (c) Look at the values of f(" }{TEXT 288 1 "x" }{TEXT -1 5 ") as " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 54 " approaches - 3 from values that are smaller than - 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "f(-3.0001); f(-3.00000001); f(-3.00000000001); f(-3.00000000000001 ); f(-3.000000000000000001);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 286 22 "Note: Other values of" }{TEXT 285 1 " " }{TEXT 256 1 "x" }{TEXT 257 41 " are possible; just so that the val ue of " }{TEXT 258 1 "x" }{TEXT 294 30 " approaches - 3 from the left. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 " (d) From your answers in \+ Parts (b) and (c), what do you think is " }{XPPEDIT 18 0 "Limit((10*x^ 3+47*x^2+54*x+9)/(6*x^3-x^2-42*x+45),x = -3)" "6#-%&LimitG6$*&,**&\"#5 \"\"\"*$%\"xG\"\"$F*F**&\"#ZF**$F,\"\"#F*F**&\"#aF*F,F*F*\"\"*F*F*,**& \"\"'F**$F,F-F*F**$F,F1!\"\"*&\"#UF*F,F*F:\"#XF*F:/F,,$F-F:" }{TEXT -1 3 " ?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 268 28 " Answer for Part (d) " }{TEXT 269 14 " 1/3 \+ " }{TEXT 270 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 " (e) Find " }{XPPEDIT 18 0 "Limit((10*x^3+47*x^2+54*x+9)/(6*x^3-x^2-42*x+45),x = -3)" "6#-%&Limit G6$*&,**&\"#5\"\"\"*$%\"xG\"\"$F*F**&\"#ZF**$F,\"\"#F*F**&\"#aF*F,F*F* \"\"*F*F*,**&\"\"'F**$F,F-F*F**$F,F1!\"\"*&\"#UF*F,F*F:\"#XF*F:/F,,$F- F:" }{TEXT -1 41 " using the Maple command to find limits." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Limit(f(x), x=-3); value(%); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 271 0 "" }{TEXT -1 7 " " }{TEXT 272 20 "Answer for P art (e) " }{TEXT 273 14 " 1/3 " }{TEXT 274 0 "" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "2. Find " }{XPPEDIT 18 0 "Limit( sin(x)/x,x = 0);" "6#-%&LimitG6$*&-%$sinG6#%\"xG\"\"\"F*!\"\"/F*\"\"! " }{TEXT -1 26 " by doing the following:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 " (a) Write the express ion " }{XPPEDIT 18 0 "sin(x)/x;" "6#*&-%$sinG6#%\"xG\"\"\"F'!\"\"" } {TEXT -1 39 " as a function g using Maple syntax. " }{TEXT 275 112 " Note: Watch your Maple syntax for writing the sine function. You wil l need parentheses around the variable of " }{TEXT 276 1 "x" }{TEXT 277 1 "." }{TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g := x -> sin(x)/x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 33 " (b) Look at the values of g(" } {TEXT 289 1 "x" }{TEXT -1 5 ") as " }{XPPEDIT 18 0 "x" "6#%\"xG" } {TEXT -1 49 " approaches 0 from values that are larger than 0." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "g(0.0001); g(0.00000001); g( 0.00000000001); g(0.00000000000001); g(0.000000000000000001);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 260 23 "Note: Other values of " }{TEXT 256 1 " x" }{TEXT 257 41 " are possible; just so that the value of " }{TEXT 258 1 "x" }{TEXT 295 29 " approaches 0 from the right." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 " (c) L ook at the values of g(" }{TEXT 287 1 "x" }{TEXT -1 5 ") as " } {XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 50 " approaches 0 from values th at are smaller than 0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "g (-0.0001); g(-0.00000001); g(-0.00000000001); g(-0.00000000000001); g( -0.000000000000000001);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 23 "Note: O ther values of " }{TEXT 256 1 "x" }{TEXT 257 41 " are possible; just s o that the value of " }{TEXT 258 1 "x" }{TEXT 296 28 " approaches 0 fr om the left." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 " (d) From your answers in Parts (b) and (c), what do you think is " }{XPPEDIT 18 0 "Limit(sin(x)/x,x = 0)" "6#-%&LimitG6$*&-%$sinG6#%\"xG\"\"\"F*!\"\"/F* \"\"!" }{TEXT -1 4 " ?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 257 28 " Answer for Part (d) " }{TEXT 278 10 " 1 " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 " (e) Find " }{XPPEDIT 18 0 "Li mit(sin(x)/x,x = 0);" "6#-%&LimitG6$*&-%$sinG6#%\"xG\"\"\"F*!\"\"/F*\" \"!" }{TEXT -1 41 " using the Maple command to find limits." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Limit(g(x), x=0); value(%); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 " " }{TEXT 261 20 "Answer for Part (e) " }{TEXT 279 12 " 1 " }}}}{MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }