Homework assignments for Math 2433-003

Homework Assignments for Mathematics 2433-003 - Honors Calculus III - Fall, 2007

  1. (due 9/4) 5.2 # 17-20, 5.3 # 53, 54, 59
  2. (9/4) 11.1 # 14, 15, 17, 24-27, 31, 11.2 # 8, 19 (graph without using a device), 29-31, 39, 42
  3. (9/4) 11.2 # 48, 52, 57, 58, 61, 66, 11.3 # 15-26, 29-32, also, be able to do 11.3 # 1-12
  4. (9/20) 11.3 # 33, 34, 41, 44 (for 44, analyze the behavior of the curve when theta is close to 0 by calculating lim r as theta -> 0 ), 47-48, 57-58, 63-64, 66-67
  5. (9/20) 11.4 # 11, 25, 26, 30, 34, 45-46, 55 (the polar axis means the x-axis)
  6. (9/20) 12.1 as many as needed of 1-40, including at least 11, 12, 14, 18, 25-29, 32-35, 39, 40
  7. (9/20) 12.1 # 54-61 (for 61, show also that the sequence is increasing and bounded)
  8. (9/20) 12.2 # 10, as many of 14-34 as needed, including at least 16, 18-21, 27-29, 41-46, 49, 53
  9. (10/4) 12.3 # 17, 18, 22-25, 28, 38, 39
  10. (10/4) 12.4 as many as needed of 3-32, including at least 9, 13, 15, 20, 29-32, 40-42
  11. (10/4) 12.5 as many as needed of 2-20, including at least 4, 7, 12-17, 35
  12. (10/4) 12.6 as many as needed of 2-28, including at least 3, 7, 11-14, 20-28
  13.            12.7 as many as needed
  14. (10/18) 12.8 as many as needed of 3-28, including at least 15, 20-21, 23, 27, 29, 30, 35, 36, 40
  15. (10/18) 12.9 as many as needed of 3-10, including at least 7-10, 13, 15-18, 23-26, 32
  16. (10/18) 12.10 # 1, 2, as many as needed of 3-18, including at least 4, 9, 11, 17, 18
  17. (10/18) 12.10 # 19, 22
  18. (10/18) Use Taylor's Theorem to verify that e^x = \sum_{n=0}^\infty x^n/n! for all x < 0.
  19. (10/18) Use Lagrange's form for the remainder to verify that cos(x) = \sum_{n=0}^\infty (-1)^n x^{2n}/(2n)! for all x.
  20. (11/6) 13.1 # 12, 18, as many as needed of 23-34 including at least 28, 31-34, 35-38, 40
  21. (11/6) 13.2 as many as needed of 1-37, including at least 18, 22, 25, 26, 29, 36, 37
  22. (11/6) 13.3 as many of 1-28 as needed, including at least 1, 11-14, 19, 23-26, 28, as many of 35-40 as needed, 39, 40, 49-52, 57, 58
  23. (11/6) 13.4 as many as needed of 1-18, including at least 6, 8-12, 15, 24, 26, 38, 39, 41, 45
  24. (11/6) 13.5 # 1, 2, 4, 10, 13, 17, 18
  25. (11/29) 13.5 # 20, 21, 27, 28, 32, 35, 42, 54, 69 (use formula 9), find a formula for the shortest distance between the lines (x_0 + a_0 t, y_0 + b_0 t, z_0 + c_0 t) and (x_1 + a_1 t, y_1 + b_1 t, z_1 + c_1 t) (Hint: find parallel planes, one containing each line, and use problem 69).
  26. (11/29) 13.6 # 13, 15, 36, 41, 42, 45
  27. (11/29) 13.7 as many as needed of 1-36, including at least 31-36, 40, 42, 43, 45, 46, 48, 53, 54
  28. (11/29) 14.1 # 1, 2, 11, 12, 19-24, 34-36
  29. 14.2 # 6, 7, 12, 15-17, 21, 25, 47, 49
  30. 14.3 # 5, 11, 13, 16, 23, 24, 28, 32, 33, 39
  31. 14.4 # 3, 5, 10, 31, 33, 35

1.	(due 9/4) 5.2 # 17-20, 5.3 # 53, 54, 59
2.	(9/4) 11.1 # 14, 15, 17, 24-27, 31, 11.2 # 8, 19 (graph without using a device), 29-31, 39, 42
3.	(9/4) 11.2 # 48, 52, 57, 58, 61, 66, 11.3 # 15-26, 29-32, also, be able to do 11.3 # 1-12
4.	(9/20) 11.3 # 33, 34, 41, 44 (for 44, analyze the behavior of the curve when theta is close to 0 by calculating lim r as theta -> 0 ), 47-48, 57-58, 63-64, 66-67
5.	(9/20) 11.4 # 11, 25, 26, 30, 34, 45-46, 55 (the polar axis means the x-axis)
6.	(9/20) 12.1 as many as needed of 1-40, including at least 11, 12, 14, 18, 25-29, 32-35, 39, 40
7.	(9/20) 12.1 # 54-61 (for 61, show also that the sequence is increasing and bounded)
8.	(9/20) 12.2 # 10, as many of 14-34 as needed, including at least 16, 18-21, 27-29, 41-46, 49, 53
9.	(10/4) 12.3 # 17, 18, 22-25, 28, 38, 39
10.	(10/4) 12.4 as many as needed of 3-32, including at least 9, 13, 15, 20, 29-32, 40-42
11.	(10/4) 12.5 as many as needed of 2-20, including at least 4, 7, 12-17, 35
12.	(10/4) 12.6 as many as needed of 2-28, including at least 3, 7, 11-14, 20-28
13.	12.7 as many as needed
14.	(10/18) 12.8 as many as needed of 3-28, including at least 15, 20-21, 23, 27, 29, 30, 35, 36, 40
15.	(10/18) 12.9 as many as needed of 3-10, including at least 7-10, 13, 15-18, 23-26, 32
16.	(10/18) 12.10 # 1, 2, as many as needed of 3-18, including at least 4, 9, 11, 17, 18
17.	(10/18) 12.10 # 19, 22
18.	(10/18) Use Taylor's Theorem to verify that e^x = \sum_{n=0}^\infty x^n/n! for all x < 0.
19.	(10/18) Use Lagrange's form for the remainder to verify that cos(x) = \sum_{n=0}^\infty (-1)^n x^{2n}/(2n)! for all x.
20.	(11/6) 13.1 # 12, 18, as many as needed of 23-34 including at least 28, 31-34, 35-38, 40
21.	(11/6) 13.2 as many as needed of 1-37, including at least 18, 22, 25, 26, 29, 36, 37
22.	(11/6) 13.3 as many of 1-28 as needed, including at least 1, 11-14, 19, 23-26, 28, as many of 35-40 as needed, 39, 40, 49-52, 57, 58
23.	(11/6) 13.4 as many as needed of 1-18, including at least 6, 8-12, 15, 24, 26, 38, 39, 41, 45
24.	(11/6) 13.5 # 1, 2, 4, 10, 13, 17, 18
25.	(11/29) 13.5 # 20, 21, 27, 28, 32, 35, 42, 54, 69 (use formula 9), find a formula for the shortest distance between the lines (x_0 + a_0 t, y_0 + b_0 t, z_0 + c_0 t) and (x_1 + a_1 t, y_1 + b_1 t, z_1 + c_1 t) (Hint: find parallel planes, one containing each line, and use problem 69).
26.	(11/29) 13.6 # 13, 15, 36, 41, 42, 45
27.	(11/29) 13.7 as many as needed of 1-36, including at least 31-36, 40, 42, 43, 45, 46, 48, 53, 54
28.	(11/29) 14.1 # 1, 2, 11, 12, 19-24, 34-36
29.	14.2 # 6, 7, 12, 15-17, 21, 25, 47, 49
30.	14.3 # 5, 11, 13, 16, 23, 24, 28, 32, 33, 39
31.	14.4 # 3, 5, 10, 31, 33, 35