{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 0 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 1 0 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 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 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 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 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 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 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 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 259 10 "MATH-1850 " }{TEXT -1 3 " " }{TEXT 260 18 "COMPUTER PROBLEM 5" }{TEXT -1 53 " DUE: Tuesday , October 10, 2000, in your lab class" }}{PARA 0 "" 0 "" {TEXT -1 17 " \nTeam members: " }{TEXT 267 54 "(All lines for answers below will e xtend 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 25 "Score: / 6\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 13 "INSTRUCTIONS " }{TEXT 257 20 "(Click b ox in front)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 1192 "It is strongly suggested that this project be worked \+ in teams (of up to 3 persons). Approaches may be discussed among diff erent teams, but each team must write their OWN report.\nREQUIREMENTS \+ OF REPORT:\n- Mathematical contents (correctness and completeness) cou nts most. Solve the problems and show all essential calculations (comm ands and output) and plots. Please do not submit work that is not esse ntial (e.g. checking out how the function fplot in Problem 1 works - t his may be essential to your understanding, but it s not essential for the reader).\n- Explain the steps you carry out. Explain the approach es/techniques that you use.\n- Add explanations and answer questions w here asked to do so. By all means, include additional explanations/obs ervations/conclusions that come to your mind! (This could translate to extra credit.)\nHOW TO SUBMIT THE REPORT\nEach team submits ONE print ed 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 ca n print from inside your Maple worksheet (choose File/Print or click o n the printer button). Set the ZOOM FACTOR to 100% (smallest magnifyin g glass) before printing.\n" }{TEXT 256 62 "Please remove these instru ctions before submitting the report." }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Graph the function " }{TEXT 268 1 "f" }{TEXT -1 1 "(" }{TEXT 269 1 "x" } {TEXT -1 4 ") = " }{XPPEDIT 18 0 "(4-3*x)/(x+2);" "6#*&,&\"\"%\"\"\"*& \"\"$F&%\"xGF&!\"\"F&,&F)F&\"\"#F&F*" }{TEXT -1 77 " and the tangent \+ line and the tangent point at the point on the graph where " }{TEXT 270 1 "x" }{TEXT -1 66 " = - 3 on one graph. Use three different colo rs for the graph of " }{TEXT 279 1 "f" }{TEXT -1 68 ", the graph of th e tangent line, and the graph of the tangent point." }{TEXT -1 57 " I n order to get to this graph, please do the following:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "(a) Defi ne the function " }{TEXT 271 1 "f" }{TEXT -1 20 " using Maple syntax: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := x -> (4-3*x)/(x+2) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "(b) Find a nic e graph of the function " }{TEXT 272 1 "f" }{TEXT -1 20 " by restricti ng the " }{TEXT 273 1 "x" }{TEXT -1 8 " and/or " }{TEXT 274 1 "y" } {TEXT -1 24 " values. Also, use the " }{TEXT 275 12 "discont=true" } {TEXT -1 80 " command so that discontinuities are not connected. Stor e this graph in memory." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " plot(f(x), x=-6..6, y=-40..40, discont=true, color=red); funct := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 59 "(c) Find the slope of the tangent line at the point where " }{TEXT 277 1 "x" }{TEXT -1 33 " = - 3 by evaluating one limit. " }{TEXT 276 50 "Don't evaluate the limit by doing it step by step." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Limit( (f(-3+h)-f(-3))/h,h=0); valu e(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "(d) Find the equation of the tangent line at the point w here " }{TEXT 278 1 "x" }{TEXT -1 7 " = - 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y = solve(y - f(-3) = -10*(x+3),y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 280 2 "OR" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "y = -10*(x+ 3)+f(-3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 91 "(e) Graph the equation of the tangent line in Part (d) a bove. Store this graph in memory." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plot(-10*x-43, x=-6..6, color=blue); tanline := %:" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 " (f) Graph the tangent point. Store this point in memory." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot( [ [-3, f(-3)] ], style=point, symbol=box, color=black); tanpt := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "(g) Display the functio n, the tangent line, and the tangent point which were stored in memory above." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "display(funct, tanline, tan pt);" }}}}{MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }