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Spring 2008

Directions: Please follow these directions on all homework assignments.

1. On each homework assignment, place your name in the top right corner of the page.
2. On the first line of the of the first page of your homework, please write down the assignment number, the pages that encompass the assignment, and list each exercise number assigned. For example, the first line of your homework might read: Assignment #12, Page 150, #1, 3, 5, 7, 8, 10, 11, 23, 45
   
3. If an assignment takes more than a page, please staple the pages together with a single staple in the upper left-hand corner.
4. Assignments will be handed in during classtime in separate piles: the assignment #1 pile, the assignment #2 pile, etc., so please do not staple two or more assignments together.
5. Simple one or two word answers or choices without explanatory prose are not acceptable. In all cases, use sound writing to justify your response.

• Assignment #1
  • Read the Syllabus
  • After logging onto Blackboard, update all your personal information. It is very important that your email address is current and correctly entered in Blackboard.
  • Once you've updated your personal information, read the welcome message on the Discussion Board and reply to the thread.
• Assignment #2
• • Start building your personal Math 50B Reference Book! Get a bound notebook with grid (graph) paper in it. Make a title page with your name and contact information, set up a table of contents, and begin some entries (number the pages, with page #1 being the first page with information on it, after leaving a few pages blank for the table of contents to grow into).
    • Bring your Reference Book to the second class meeting on Wednesday and show me your title page, toc, and beginning page.
    • Throughout the semester, you should enter important information in your Reference Book, such as definitions, procedures, key examples, explanations that make sense to you, diagrams -- ANYTHING that you anticipate will be USEFUL to you as we proceed in this course ... and beyond! This is FOR YOU. In particular, your Reference Book should serve as a very useful study guide for quizzes and exams. (Note, however, that your Reference Book is not a substitute for class notes. In general, your Reference Book should be much more concise and organized than your class notes, which normally contain everything that we do in class.)
    • Each time we have an examination, I will collect your Reference Book and assign it a grade. In addition, although the final examination is closed book and closed notes, you will be allowed to use your Reference Book on the final exam.
• Assignment #3
  • Read Section 5.3.
  • Pages 402-403, do exercises #7, 11, 13, 15, 49, and 51.
• Assignment #4
  • Read Section 5.5.
  • Pages 420-421, do exercises #7, 11, 13, 21, 25, 31, 35, 37, 41, 51, 55, 57, 63, 73, and 74.
• Geogebra
  • A very nice piece of software for generating graphs is called Geogebra and can be downloaded at http://www.geogebra.org/cms/.
• Winiplot
  • Another nice piece of software for generating graphs is called Winplot and can be downloaded at http://math.exeter.edu/rparris/winplot.html/.
• Assignment #5
  • Read Section 6.1.
  • Pages 442-443, do exercises #7, 9, 17, 19, 20, 24, 27, 44, 45, and 49.
• Assignment #6
  • Read Section 6.2.
  • Page 452, do exercises #1, 5, 16, and 17. In each case, provide two sketches: (1) the region in the plane with typical strip, and (2) the solid showing typical disk or washer.
  • Pages 453-454, do exercises #48, 49, 55, and 58. In each case sketch the solid and typical cross section. Provide any other sketches you deem necessary for the solution of the exercise.
  • Page 454, do exercises #61 and 68. Provide any sketches necessary for the solution of each exercise.
• Assignment #7
  • Read Section 6.3.
  • Pages 458-459, do exercises #5, 6, 13, 14, 17, and 20. In each case, provide two sketches: (1) the region of interest in the plane with typical strip, and (2) the solid of revolution with the typical cylindrical shell.
  • Page 459, do exercises #43, 44, and 45. In each case, provide all needed sketches
• Some Advice on Techniques of Integration
  • You are going to feel the level of difficulty kick up a notch in Chapter 7. It is important to stay current with your homework and work through some frustration.
  • Sometimes students can get down on themselves when they see their instructor working though problems with seeming ease at the blackboard and whiteboard, yet they struggle mightily. Note that you are not alone in your frustration. It is important to understand that your instructors went through the same agonizing periods of difficulty when they first encountered the material in Chapter 7. If it seems like they pour through solutions at the board with ease, please know that it was not always so. Your struggles are perfectly understandable at this stage. Work together on solutions and ideas. Ask for help in the Mathlab, during office hours, and post questions on the discussion board.
  • Finally, there is only one way I know of getting good at a particular thing, and that's through practice, practice, and more practice. Try to do as many problems as you possibly can, even beyond the ones assigned for homework.
• Exam #1
  • You can download Exam #1. The exam is due at the beginning of class on Monday, February 11, 2008.
• Assignment #8
  • Read Section 7.1.
  • Pages 480-481, do exercises #4, 7, 9, 10, 11, 12, 13, 16, 24, 29, 30, 34, 42, 43, 48, and 61. Show detailed steps in each solution. I'm not interested in what your calculator or computer gathers as the answer, although feel free to check your answer in this mannner.
• Assignment #9
  • Read Section 7.2.
  • Pages 488-489, do exercises #1, 8, 9, 11, 14, 16, 17, 20, 24, 26, 29, 34, 41, 43, 65, 66, 67, and 68. Show detailed steps in each solution. I'm not interested in what your calculator or computer gathers as the answer, although feel free to check your answer in this mannner.
• Assignment #10
  • Read Section 7.3.
  • Pages 494-495, do exercises #6, 7, 16, 25, 27, 28, 31, 39, and 40. Show detailed steps in each solution. I'm not interested in what your calculator or computer gathers as the answer, although feel free to check your answer in this mannner.
• Assignment #11
  • Read Section 7.4.
  • Pages 504, do exercises #8, 12, 19, 25, 32, 35, 39, and 50. Show detailed steps in each solution. I'm not interested in what your calculator or computer gathers as the answer, although feel free to check your answer in this mannner.
• Assignment #12
  • Read Section 7.6.
  • Pages 516, do exercises #6, 9, 17, and 27.
  • Pag 516, use a computer algebra system to evaluate the given integral in exercise #35. Then use the table of integrals to perform the integration. Show that the answers obtained by the two methods are the same.
    • Note: You have a number of options here.
      1. You can obtain a login and password from your instructor. You can then use either Matlab or Maple on the machines in PS116 to evaluate the integral.
      2. Here is an online integrator:
         http://integrals.wolfram.com/index.jsp

• Exam #2
  • Download Exam #2. This exam is due Monday, March 3, at the beginning of class.
• Assignment #13
  • Read Section 7.7.
  • Use the instructions in left.pdf to program your calculator to use the left endpoint method. Use the program to find the area under the curve y = x² on the interval [0, 2].
  • Use the instructions in right.pdf to program your calculator to use the right endpoint method. Use the program to find the area under the curve y = x² on the interval [0, 2].
  • Use the instructions in midpoint.pdf to program your calculator to use the midpoint method. Use the program to approximate the integral in exercise #7 on page 527.
  • Use the instructions in trap.pdf to program your calculator to use the trapezoid method. Use the program to approximate the integral in exercise #7 on page 527.
  • Use the instructions in simp.pdf to program your calculator to use the Simpson's method. Use the program to approximate the integral in exercise #7 on page 527.
• Assignment #14
  • Read Section 7.8.
  • On page 538, do exercises #5, 10, 11, 14, 28, 34, and 37. In each case, use your calculator (alternately, use WinPlot or Geogebra) to sketch the integrand over the interval dictated by the upper and lower bounds of the integral. Obtain a printout (in the case of Winplot or Geogebra) or make a copy on your homework paper from your calculator.
  • Use Winplot or Geogebra to sketch the graphs of f and g on the interval indicated in exercises #47 and 48. Obtain a printout, then answer each of the questions posed in these exercises.
  • On page 539, do exercises #60, 61, and 71. Show all of your work.
• Assignment #15
  • Read Section 8.1.
  • On page 552, do exercises #5, 10, 13, and 14. Use Winplot or Geogebra to sketch the graph of the curve on the given interval. Use your graph to approximate the length of the curve and compare with your exact solution.
  • Page 553, do exercise #21. Use Winplot or Geogebra to sketch the curve on the given interval. Use your Simpson program on your calculator to estimate the integral for n = 10. Then use the built-in integrator on your calculator to estimate the integral and compare to the result captured by your Simpson program.
  • Page 553, do exercise #29. Prove that the graph is symmetric with respect to the x- and y-axes. Find the exact length of the part of the curve that lies in the first quadrant, then use symmetry to determine the total length of the curve. Provide a plot generated by either Winplot of Geogebra.
  • Page 553, do exercise #30. Sketch the curve on the given interval by hand. To do this, use the first derivative test to determine where the function is increasing or decreasing on the given interval. Then use the second derivative test to determine where the function is concave up or down on the given interval. Once you've completed the sketch, follow the rest of the directions in the problem statement exactly. Find exact integrals.
  • Page 553, do exercise #36. Provide a Winplot or Geogebra sketch of your final result.
• Assignment #16
  • Read Section 8.2.
  • On page 559, do exercises #10, 11, and 16. Use Winplot to sketch the surface of revolution for the given curve on the given interval.
  • Page 559, do exercise #18. Use Winplot or Geogebra to sketch the surface of revolution for the curve on the given interval. Use your Simpson program on your calculator to estimate the surface area for n = 10. Then use the built-in integrator on your calculator to estimate the integral and compare to the result captured by your Simpson program.
  • Page 560, do exercises #29 and 30. Include detailed sketches with your solution.
• Assignment #17
  • Read Section 11.1.
  • On page 710-711, do exercises #5, 8, 10, and 12.
  • Page 711, do exercises #15-39 odd. Note: It is not enough to provide an answer. You must also give very good reasons for your answer, so show all of your work.
  • Page 711, use Winplot to sketch the sequences in exercises #41, 43, 44, 46, and 48. If the sequence is convergent, show solid work that supports your estimated limit as the exact answer.
  • Page 711-712, do exercises #51, 61, 62, 63, and 64. Show supporting work.
• Assignment #18
  • Read Section 11.2.
  • On page 720, do exercises #11-33 odd. Note: It is not enough to provide an answer. You must also give very good reasons for your answer, so show all of your work.
  • Pages 720-721, do exercises #38, 39, 43, 44, 46, 47, and 55. Note: It is not enough to provide an answer. You must also give very good reasons for your answer, so show all of your work.
  • Page 722, do exercise #57.
• Exam #3
  • Download Exam #3. This exam is due Monday, March 24, at the beginning of class.
• Assignment #19
  • Read Section 11.3.
  • On page 729, use the integral test to determine whether the series in exercises #3 and 5 converge or diverge.
  • Pages 729, do exercises #9-23 odd. In each case, it is not sufficient to simply say that the series "converges" or "diverges". You must give a valid reason for your answer. This might have to do with an integral test, an n^th term test, etc., but you must have a rigorous explanation for your reply.
  • O pages 729-730, find the requested p-value in exercises #25 and 27. Hand calculations only, please!
  • On page 730, do exercises #31, 35, and 37.
• Assignment #20
  • Read Section 11.4.
  • On page 734-735, do exercises #3-35 (odd). In each case, bring some mathematical power to bear, such as examining the n^th term and the sequence of partial sums in Winplot. Analytically, provide a careful writeup of your explanation for convergence of divergence. Show all of your work. A simple "converges" or "diverges" is completely unacceptable.
• Assignment #21
  • Read Section 11.5.
  • On page 739, do exercises #3-19 (odd). In each case, bring some mathematical power to bear, such as examining the n^th term and the sequence of partial sums in Winplot. Analytically, provide a careful writeup of your explanation for convergence of divergence. Show all of your work. A simple "converges" or "diverges" is completely unacceptable.
  • On page 739, do exercises #21 and 22. Obtain printouts of of the plots of the sequence of terms and sequence of partial sums and include the printout with your homework papers.
  • On page 739-740, do exercises #23 and 27. Give good reasons for your solution. Show your work.
• Assignment #22
  • Read Section 11.6.
  • On pages 745-746, do exercises #3-27 (odd). In each case, bring some mathematical power to bear, such as examining the n^th term and the sequence of partial sums in Winplot. Analytically, provide a careful writeup of your explanation for convergence of divergence. Show all of your work. A simple "converges" or "diverges" is completely unacceptable.
  • On page 746, do exercises #29, 32, and 33. Give good reasons for your solution. Show your work.
• Assignment #23
  • Read Section 11.7.
  • On page 748, do exercises #1, 5, 9, 13, 17, 21, 25, 29, 33, and 37. In each case, bring some mathematical power to bear, such as examining the n^th term and the sequence of partial sums in Winplot. Analytically, provide a careful writeup of your explanation for convergence of divergence. Show all of your work. A simple "converges" or "diverges" is completely unacceptable.
• Assignment #24
  • Read Section 11.8.
  • On page 753, do exercises #1-27 (odd), and 31 Show all supporting work.
  • On pages 753-754, do exercises #32, 33, and 34. Use Winplot to show the plot of the partial sums requested as well as the function to which they converge.
• Assignment #25
  • Read Section 11.9.
  • On page 759, do exercises #3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 33, 39, and 40.
• Assignment #26
  • Read Section 11.10.
  • On page 770, do exercises #6, 8, 9, 11, 13, and 17.
  • On page 771, do exercise #33. Use Winplot to provide a printout of the requested plot.
  • On page 771, exercise #37, use the remainder term to evaluate e^(-0.02) correct to five decimal places.
• Assignment #27
  • Read Section 11.12.
  • On page 783, perform each of the following tasks for exercises #3, 8, and 9:
    1. Compute the requested Taylor polynomial.
    2. Sketch the Taylor polynomial and the given function on the same screen using Winplot. Include a printout with your homework papers.
  • On page 83, perform each of the following tasks for exercises #13, 15, and 21:
    1. Compute the requested Taylor polynomial.
    2. Use Taylor's Inequality to estimate the accuracy of the approximation when x lies in the given interval.
    3. Sketch |R_n(x)| using Winplot and use the plot to compare the error in part (2).
• Assignment #28
  • In Stewart, Early Transcendentals, read Section 10.1, pages 650-656.
  • In Stewart, Early Transcendentals, pages 656-659, do exercises #12, 13, 14, and 17 by hand.
  • In Stewart, Early Transcendentals, page 658, do all parts of exercise #33. Use your calculator to verify your results.
  • In Stewart, Early Transcendentals, page 658, do exercises #38 and 39 by hand. Please include labeled sketches with your solutions.
  • In Stewart, Early Transcendentals, page 658, use Geogebra to sketch the locus of point P in exercise #40 as point A moves about the outer circle. Then find parametric equations of the locus by hand. Please include a labeled sketch with your solution. Finally, plot your resulting parametric equations in Winplot or Geogebra and compare it to the result found using the Geogebra. Include printed plots with your solution.
  • In Stewart, Early Transcendentals, page 659, exercise #43, use Winplot or Geogebra to plot the curves presented by the given parametric equations. Follow the remainder of the directions.
• Assignment #29
  • In Stewart, Early Transcendentals, read Section 10.2, pages 660-666.
  • In Stewart, Early Transcendentals, page 667, do exercise #31. Please include a detailed sketch with your work. This can be drawn by hand if you wish, or you may use Geogebra or Winplot.
  • In Stewart, Early Transcendentals, page 667, do exercise #34. Use Winplot or Geogebra to draw a sketch of the Astroid for a = 2, but use the constant a in your calculation.
  • In Stewart, Early Transcendentals, page 667, use Winplot or Geogebra to sketch the arcs in exercises #45 and #48. Then use hand calculations to determine the arc length.
  • In Stewart, Early Transcendentals, page 667, do exercise #50. Use Geogebra to draw the witch over the given region with a = 2.
  • In Stewart, Early Transcendentals, page 668, do exercise #62. Use Winplot or Geogebra to draw the curve in the plane over the interval appropriate for the task at hand.
  • In Stewart, Early Transcendentals, page 668, do exercise #73, but follow these directions:
    1. First, find the coordinates (x,y) of point P in terms of theta, and verify that your result matches the given result in the text. That is, you may not assume that the equations given are correct. You must prove that the given equations are correct.
    2. Use the Geogebra to draw the image.
    3. Perform the appropriate integration to find the length of the involute as theta ranges from 0 to 2π.
• Exam #5
  • Download Exam #5. Due Tuesday, 5/6.