There are files on this site in PDF format. You will need to download a free copy of the Acrobat Reader to read them. Click the following icon to obtain a free copy of the Acrobat Reader.

It is important that you have the most current version of the Acrobat Reader that your system will allow. The above links will take you to the Adobe site. Your system will be automatically analyzed and you will be informed of the optimal version of the reader for your system.

Fall 2007

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.
6. Read and use the following Homework Guidelines.

• 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 50A 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 2.1 in Stewart.
  • Pages 91 and following, do exercises #1, 3, 5, 8, and 9.
• Assignment #4
• • Read Section 2.2 in Stewart.
  • Pages 102 and following, do exercises #4, 7, 9, 11, 12, 13, 19, 21, 28, 29, 30, 33, and 39.
• Quiz #1
• • Quiz #1 is due Monday 9/10/07.
  • Download Quiz #1
• Assignment #5
• • Read Section 2.3 in Stewart.
  • Pages 111 and following, do exercises #2, 11, 15, 17, 19, 21, 25, and 28.
  • On page 112, use Winplot or Geogebra to draw the graphs requested for exercises #31, 33, and 34, 35.
  • On pages 112-113, do exercises #37, 38, 40, 41, 43, 44, and 47.
  • On page 112, you might try to use Geogebra or the Geometer's Sketchpad (available on the campus computers in PS116) to create the dynamic image in exercise #60. Then solve #60.
• Assignment #6
• • Read Section 2.4 in Stewart.
  • Pages 122 and following, do exercises #3, 4, 5, 6, 7, 11, 12, 15, 23, 24, 31, 37, 39, and 43.
• Assignment #7
• • Read Section 2.5 in Stewart.
  • Pages 133 and following, do exercises #3, 5, 6, 15, 19, 29, 41, 43, 45, 46, 51, and 62.
• Assignment #8
• • Read Section 2.6 in Stewart.
  • Pages 146, exercise #3, first copy the image onto graph paper, then compute each of the requested limits.
  • Page 146-147, do exercises #11, 15, 17, 21, 23, 31, 32, and 34. In each exercise, show all of the required work and state any theorems you are using.
  • Page 147, exercise #35, answer each part of the exercise. Use either Winplot or Geogebra to draw a graph showing all of the important features of the function. In part (b), show the tabular work you used to determine the limit. In part (c), use a completely symbolic or analytical approach to determine the limit.
  • Page 147, in exercises #37, 40, 41, and 42, first use a symbolic or analytical approach to determine the limit. Show you work. Then use either Winplot or Geogebra to sketch the graph (including asymptotes). Explain how the graphs shows the same limit as your analytical approach provided.
• Quiz #2
• • Quiz #2 is due Monday 9/17/07.
  • Download Quiz #2
• Assignment #9
• • Read Section 2.7 in Stewart.
  • Pages 155, do exercise #1. Include a sketch that explains the calculations you are making in the exercise.
  • Page 155, copy the image in exercise #3 onto your homework, then answer the question posed in the exercise. Place tangent lines at each point to help with your explanation.
  • Page 155, use Winplot or Geogebra to perform the tasks demanded in exercise #4.
  • Page 156, use symbolic calculations only to determine the slope and equation of the required tangent line in exercises #7 and 9.
  • Page 156, use symbolic calculations to determine the slope and equations of the requested tangent lines in exercises 13 and 14, parts (a) and (b). In part (c) of each exercise, use either Winplot or Geogebra to draw the graph of the function and the tangent lines found in part (b) of each exercise.
  • Page 156, determine the requested instantaneous velocity in exercise #17 by using symbolic calculations only.
  • Page 156, determine the average and instantaneous velocities requested in parts (a) and (b) of exercise #20, using symbolic calculations only. Then, use either Winplot or Geogebra to plot the function, the secant, and tangent lines representing the average and instantaneous velocities found in parts (a) and (b). Please do all of the secant and tangent lines on one plot.
• Assignment #10
• • Read Section 2.8 in Stewart.
  • Page 163, sketch the graph given in exercise #3, then answer the questions posed. Annotate your plot to explain your reasoning.
  • Page 163, exercises #4 and 5, sketch (by hand) the requested graphs on graph paper.
  • Page 163, follow the given directions for exercise #9 but use Winplot or Geogebra to draw and the graph of the given function and the tangent line at the given point. Obtain a printout of the result.
  • Page 163-164, do exercise #11. Use Winplot or Geogebra to zoom in and estimate the slope. Annotate your plot and explain your answer.
  • Page 163, use symbolic calculations and the definition of the derivaive to determine the value of f^'(a) in exercises #15 and 17.
  • Page 163, do exercises #19, 23, and 25.
• Assignment #11
• • Read Section 2.9 in Stewart.
  • Pages 173-174, perform each of the following tasks for exercises #5, 7, 11, and 13.
    1. Sketch the given function on a sheet of graph paper in blue.
    2. On the same coordinate system as the graph of the given function, sketch the derivative of the function in red.
  • Page 174, do exercises #21, 23, and 25.
  • Page 174, perform each of the following tasks for exercises #32 and 34.
    1. Follow each of the given directions in the text.
    2. Use Winplot or Geogebra to draw the graphs of the given function and its derivative on the same coordinate system.
  • Page 175, do exercise #42. Use Winplot or Geogebra to draw the graph of the given function.
  • Page 175 do exercise #43. Sketch the required graph on graph paper by hand.
• Exam #1
• • Exam #1 will be held in class Friday, September 21, 2007.
  • Download Review Questions for Exam #1
• Assignment #12
• • Read Section 3.1 in Stewart.
  • Page 191, differentiate the functions given in exercises #3-31 (odd only).
  • Page 191, perform each of the following tasks for exercise #41.
    1. Use the derivative to find the equation of the requested tangent line.
    2. Use Winplot or Geogebra to sketch the graph of the given function and its tangent line at the given point. Obtain a printout of the result.
  • Page 191-192, exercises #48, 49, and 51, perform each of the following tasks.
    1. Use the derivative to find the requested information. Show all of your work.
    2. Verify your results by sketching the results in Winplot or Geogebra. Make sure that your sketch demonstrates what is required in the problem statment. Obtain a printout.
  • Page 192, perform each of the following tasks for exercises #55.
    1. Sketch the graphs of f and the derivative of f on graph paper (by hand).
    2. Use the definition of the derivative to investigate the differentiability of f at x=1.
  • Page 192, perform each of the following tasks for exercise #57.
    1. Sketch the graph of f by hand on graph paper.
    2. Determine the derivative of f. Use the definition of the derivative to investigate the derivative of f at x=-3 and x=3.
    3. Sketch the graph of the derivative of f on the same coordinate system in a different color.
• Assignment #13
• • Read Section 3.2 in Stewart.
  • Page 197, differentiate each of the function in Exercises #3-21 (odd only).
  • Page 197, find the equation of the tangent line in Exercises #25 and 27, then use Winplot or Geogebra to draw the function and its tangent line at the given point. Obtain a printout.
  • Pages 197-198, do exercises #31 and #36.
  • Page 198, find all of the requested tangent lines for exercise #41. Use Winplot or Geogebra to draw the given function and the requested tangent lines. Obtain a printout.
  • Page 198, do all parts of exercise #44.
• Assignment #14
• • Read Section 3.3 in Stewart.
  • This assignment will not be graded, but you need to at least give this section a read.
• Assignment #15
• • Read Section 3.4 in Stewart.
  • Page 216, do exercises #1-15 (odd only).
  • Page 216, complete the proof in exercise #20 using the definition of the derivative as we did in finding the derivative of f(x) = sin(x). This will not entail deriving any new limits that we have not yet seen. You have all the limits at your disposal that you need to complete this proof.
  • Page 216-217, do exercises #25, 28, 32, and 34. Use Winplot or Geogebra to draw any requested graphs and obtain a printout of the result.
  • Page 217, do exercises #35, 37, 38, 42, 43, and 47.
• Assignment #16
• • Read Section 3.5 in Stewart.
  • Page 224, do exercises #7-41 (odd only).
  • Page 225, do exercise #47. Use Winplot or Geogebra to obtain a printout of the plot of the graph and tangent line.
  • Page 225, do exercise #51 and 52. Use Winplot or Geogebra to obtain a printout of the plot of the graph and horizontal tangent lines.
  • Page 225, do exercise #55.
  • Page 225, make an exact copy of the graphs of f and g given in exercise #57 on graph paper, then use the graphs to answer the questions posed in exercise #57.
  • Page 226, do exercise #69. Use Winplot or Geogebra to obtain a printout of the position and velocity on the same graph. Label and/or use distinct line styles (or color if you have a color printer).
  • Page 227, do exercise #75.
  • Page 227, do exercise #80. Use Winplot or Geogebra to obtain printouts of the plots of f and f' on the same plot, then g and g' on the same plot.
• Quiz #3
• • Quiz #3 is due Monday 10/15/07.
  • Download Quiz #3
• Assignment #17
• • Read Section 3.6 in Stewart.
  • Page 233, do exercises #11, 13, 15, 17, 18, 19, and 20.
  • Page 234, do exercises #25 and 27.
  • Page 234, do exercise #31. Use Winplot or Geogebra to plot the curve and its tangent line. Obtain a printout.
  • Page 234, do exercises #36, 41, 43, 47, and 49.
  • Page 235, do exercise #54.
  • Page 235, do exercises #59 and 61. Use Winplot or Geogebra to obtain a printout of the families of orthogonal trajectories. Obtain a printout.
  • Page 235, do exercise #64. Use Winplot or Geogebra to sketch the ellipse and its normal line. Obtain a printout.
• Assignment #18
• • Read Section 3.7 in Stewart.
  • Page 240, do exercises #1, 3, 15, 16, 17, 19, and 20.
  • Page 240, do exercise #21. Use Winplot or Geogebra to draw the graphs of f, f', and f''. Label your plot. Obtain a printout.
  • Page 241, do exercises #29, 31, 33, and 35.
  • Page 241, do exercise #49. Use Winplot or Geogebra to draw the graphs of the position, velocity, and acceleration over the requested time interval. Label your plot. Obtain a printout.
  • Page 241-242, do exercise #51, 53, 66, and 67.
• Assignment #19
• • Read Section 3.8 in Stewart.
  • Page 249, do exercises #3, 5, 7, 11, 17, 21, 23, 24, 28.
  • Page 249, do exercise #34. Use Winplot or Geogebra to draw the curve and its tangent lines. Label your plot. Obtain a printout.
  • Page 249, do exercises #35, 38, 41, 43, 45, 47, and 48.
• Assignment #20
• • Read Section 3.10 in Stewart.
  • Pages 260-262, do exercises #8, 9, 19, 20, 23, 29, 31, 34, and 37.
• Quiz #4
  • Quiz #4 is due Monday 10/29/07.
  • Download Quiz #4
• Assignment #21
• • Read Section 3.11 in Stewart.
  • Page 267, perform each of the following tasks for exercises #9 and 10.
    1. Use Winplot or Geogebra to draw the function and its linearization at the given point.
    2. Find the requested approximations using your linearization.
  • Page 267, perform each of the following tasks for exercise #14.
    1. Create a diagram similar to those shown in Figures 4 and 5 of Example 3 on page 264.
    2. Use Winplot or Geogebra to find and label appropriate intersection points.
    3. State the interval requested by the exercise.
  • Page 268, do exercises 17, 19, 25, and 26.
  • Page 268, perform each of the following tasks for Exercise #28.
    1. Using Winplot or Geogebra , try to construct an image similar to that in Figure 6 on page 265. You should be able to at least draw the function and its linearization, but try to add more of the detail.
    2. Whatever you cannot figure out to do with Winplot may be completed by hand using pencil and ruler.
  • Page 268, do exercises #33, 35, 41, 43, 44, and 46.
• Exam #2
  • Exam #2 is Wednesday 10/31/07.
  • Download Review Notes for Exam #2.
• Assignment #22
  • Read Section 4.1.
  • Page 287, use differentiation, algebra, and trig to find the critical values for the functions in exercises #33, 35, 37, 38, 41, 43, and 44.
  • Page 287, find the absolute max and min for the functions in exercises 57, 59, and 60 on the given interval.
  • Page 287, do exercise #63.
  • Page 287, perform each of the following tasks for exercises #65, 66, 67, and 68.
    1. Sketch the function in Winplot or Geogebra on the given interval only. In Geogebra, you would enter f = Function[x^3 - 8*x + 1, -3,3] in the Input window to limit the function f(x) = x³ - 8x + 1 to the domain [-3, 3].
    2. In Geogebra, you can enter Extremum[f] to find the extrema of the function f. Winplot has a similar utility for finding extrema on its menus. Use the text tool to annotate your plot with the resulting coordinates.
    3. Use the calculus and the Extreme Value Theorem to find the exact absolute extrema. Compare with the approximations found in part (2).
  • Page 288, do exercise #75.
• Assignment #23
  • Read Section 4.2.
  • Page 295, perform each of the following tasks for exercise #2.
    1. Use Winplot or Geogebra to draw the graph of f on the given interval. In Geogebra, you would enter f = Function[x^3 - 3*x^2 + 2*x + 5, 0, 2] in the Input window to limit the function f(x) = x³ - 3x² + 2x + 5 to the domain [0,2]. Using the graph, explain why the function satisfies each of the conditions in the hypothesis of Rolle's Theorem. Annotate your graph with your reasons (use pencil).
    2. In Geogebra, you can enter Extremum[f] to determine where f has derivative zero as predicted by Rolle's Theorem. Winplot has a similar utility for finding extrema on its menus. Use the software tools to draw horizontal tangent lines at each extrema.
    3. Use the calculus to determine the exact values 'c' such that f(c) = 0, as predicted by Rolle's Theorem. Compare with the approximations found by Winplot.
  • Page 295, do exercise #5.
  • Page 295, use Winplot or Geogebra to perform the tasks outlined in Exercise #9. Please show all of the appropriate calculus derivations in your hand-written supporting work.
  • Page 295, do exercises #12, 14, 15.
  • Page 295, exercise #19, use Winplot or Geogebra's slider feature to explore the given function for various values of 'c'. In Geogebra, proceed as follows:
    1. Enter c=0.
    2. Enter f=Function[x^3 - 25*x + c, -2, 2].
    3. Ctrl+click c=0 and select "Show object" from the popup menu. You an then use the slider that appears to adjust the value of c. You can also Ctrl+click c=0, then select properties, then the Slider tab, then adjust the min, max, and step size of the slider.
    Finally, use the calculus to prove the requested result in the problem statement.
  • Pages 295-296, do exercises #21, 27, 29, 30, and 33.
• Assignment #24
  • Read Section 4.3.
  • Page 305, do exercise #31.
  • Page 305-306, do exercises 33, 35, 41, 45, 50, 51, 61, 62, 63, and 72. Check your work with a plot in Winplot or Geogebra. Obtain a printout.
• Assignment #25
  • Read Section 4.4.
  • Page 313-314, do exercises #5-61 (odd only). In the case of exercises #37, 51, 57, and 61, use Winplot to validate your answer.
• Quiz #5
  • Quiz #5 is due Monday 11/19/07.
  • Download Quiz #5
• Assignment #26
  • Read Section 4.7.
  • Page 337, do exercises #11, 17, 19, 23, 25, 28, and 31. Use Winplot or Geogebra when you feel it might help with understanding the problem/solution.
• Quiz #6
  • Quiz #6 is due Monday 11/26/07.
  • Download Quiz #6
• Assignment #27
  • Read Section 4.10.
  • Pages 358-359, do exercises #11, 14, 27, 29, 31, 32, 37, 41, 47, 49, 59, 63, 64, 69, and 77.
• Assignment #28
  • Read Section 5.1.
  • Read Section 5.2.
  • Pages 390-391, do exercises #1, 3, 15, 16, 21, 23, 25, 26, 27, 33, 35, 37, 39, 41, 42 43, 45, 47, 48, 49, 50, 55, 61, and 65.
• Assignment #29
  • Read Section 5.3.
  • Pages 402-404, do exercises #3, 7-42(odd), 49, 51, 53, 58, 61, 67, and 68.
• Assignment #30
  • Read Section 5.5.
  • Pages 420-421, do exercises #7-69(odd) and #73.