{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 12 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 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{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 -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 0 0 0 8 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 259 10 "MATH-1850 " }{TEXT -1 3 " " }{TEXT 260 21 "COMPUTER PROBLEMS 7&8" }{TEXT -1 56 " DUE: Th ursday, November 2, 2000, in your lab class" }}{PARA 0 "" 0 "" {TEXT -1 17 "\nTeam members: " }{TEXT 267 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 261 0 "" }{TEXT -1 0 "" }{TEXT 264 17 " SOLUTION " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (2) " }{TEXT 262 0 "" }{TEXT -1 0 "" }{TEXT 265 9 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (3) " }{TEXT 263 0 "" }{TEXT -1 0 "" }{TEXT 266 9 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Score: / 6 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Score : / 6" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 33 "INSTRUCT IONS (Click box in front)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1192 "It is strongly suggested that this proj ect be worked in teams (of up to 3 persons). Approaches may be discus sed among different teams, but each team must write their OWN report. \nREQUIREMENTS OF REPORT:\n- Mathematical contents (correctness and co mpleteness) counts most. Solve the problems and show all essential cal culations (commands and output) and plots. Please do not submit work t hat is not essential (e.g. checking out how the function fplot in Prob lem 1 works - this may be essential to your understanding, but it s no t essential for the reader).\n- Explain the steps you carry out. Expla in the approaches/techniques that you use.\n- Add explanations and ans wer questions where asked to do so. By all means, include additional e xplanations/observations/conclusions that come to your mind! (This cou ld translate to extra credit.)\nHOW TO SUBMIT THE REPORT\nEach team su bmits ONE printed copy (stapled) by the due date. (Please save the ele ctronic version, as you will be asked to submit that, too, at a future time.)\nYou can print from inside your Maple worksheet (choose File/P rint or click on the printer button). Set the ZOOM FACTOR to 100% (sma llest magnifying glass) before printing.\n" }{TEXT 256 62 "Please remo ve these instructions before submitting the report." }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 7 "PROBLEM" }{TEXT -1 1 " " }{TEXT 278 1 "7" }{TEXT -1 73 " Find \+ the equation of the tangent line(s) to the graph of the function " } {TEXT 256 1 "y" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "2*x/(3*x-4);" "6#*( \"\"#\"\"\"%\"xGF%,&*&\"\"$F%F&F%F%\"\"%!\"\"F+" }{TEXT -1 42 " which passes through the point (3, - 5)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "(a) Define the function " } {TEXT 272 1 "y" }{TEXT -1 20 " using Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "y := x -> (2*x)/(3*x - 4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "(b) Find a nice graph of the f unction " }{TEXT 273 1 "y" }{TEXT -1 20 " by restricting the " }{TEXT 257 1 "x" }{TEXT -1 8 " and/or " }{TEXT 258 1 "y" }{TEXT -1 8 " values ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(y(x), x=0..4, y=- 20..20, discont=true, color=red); funct := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "(c) Find the " } {TEXT 271 5 "exact" }{TEXT -1 14 " value of the " }{TEXT 269 1 "x" } {TEXT -1 57 "-coordinate of the point(s) on the graph of the function \+ " }{TEXT 274 1 "y" }{TEXT -1 58 " where the tangent line passes throug h the point (3, - 5)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "so lve(D(y)(x)=(y(x)+5)/(x-3)); sol := %;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 270 20 "Answ er to Part (c): " }{XPPEDIT 18 0 "20/17;" "6#*&\"#?\"\"\"\"# " 0 " " {MPLTEXT 1 0 52 "y = D(y)(sol[1])*(x - sol[1]) + y(sol[1]); evalf(%) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "y = D(y)(sol[2])*(x - \+ sol[2]) + y(sol[2]); evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 280 9 "PROBLEM 8 " }{TEXT -1 21 " Graph the function " }{TEXT 279 0 "" }{TEXT 276 1 "y " }{TEXT -1 122 ", the tangent line(s) in Part (d) of PROBLEM 7, and t he point (3, - 5) on one graph. Use different colors for each graph. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 132 "plot([D(y)(sol[1])*(x- sol[1])+y(sol[1]), D(y)(sol[2])*(x-sol[2])+y(sol[2])], x=0..4, y=-20. .20, color=[blue,green]); tanlines := %:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot( [ [3, -5] ], style=point, symbol=box, color=bla ck); pt := %:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(funct, tanlin es, pt);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }