Homework assignments for Math 112: Calculus II

Chapter 3:

• Page 233 (Ch 3, sec 6): 3, 6, 9, 17, 18, 29, 38 (Hint: Find the equation of the tangent line when x=a), 44, 49, 50, 53. (Solutions)

Chapter 4:

• Page 313 (Ch 4, sec 4): 1, 2, 3, 4, 6, 7, 11, 15, 16, 26, 36, 43 (this is the log times the tangent, not the log of the quantity "x times the tangent"), 47, 56, 59, 69, 70. (Solutions)

Chapter 6:

• Page 452 (Ch 6, sec 2): 2, 3, 5, 12, 16, 20, 30, 31, 33, 45, 49, 53, 56. (Solutions)
• Page 458 (Ch 6, sec 3): 3, 5, 7, 13, 18, 20, 23, 38, 41. (Solutions)
• Page 463 (Ch 6, sec 4): 2, 6, 8 (Convert cm to m, because N and J are defined in terms of m, not cm.), 9 (First find the spring constant k by finding the work done in stretching the spring the first 10 cm in terms of k and setting the result equal to 2.), 15, 16, 20, 23 (You can break the answer into two integrals; one can be evaluated by substitution, and the other by noting that it is related to the area of a circle -- we can't find the antiderivative of that integrand yet.). (Solutions)

Chapter 7:

• Page 480 (Ch 7, sec 1): 1, 4, 6, 11, 20, 33, 41, 46, 52, 56, 59, 61. (Solutions)
• Page 488 (Ch 7, sec 2): 5, 8, 15, 20, 23, 26, 34 (See the integral of secant cubed, done in class.), 39, 42, 54, 60. (Solutions)
• Page 494 (Ch 7, sec 3): 2, 4, 5, 6, 16, 23, 26, 30, (Solutions)
• Page 504 (Ch 7, sec 4), first assignment: 2, 3, 8, 12, 15, 25, 30, 32. (Solutions)
• Page 504 (Ch 7, sec 4), second assignment: 40, 44, 47, 55, 57. (Solutions)
• Page 537 (Ch 7, sec 8): 2, 3, 5, 13, 16, 17, 20, 23, 28, 35, 38, 49, 53, 57, 61, 65 (The total work done on the rocket by gravity, as the distance goes from to infinity must be equal to the initial kinetic energy.), 71 (In computing the integral, s is a constant. In finding the domain of F, it is a variable.), 72. (Solutions)

Chapter 8:

• Page 552 (Ch 8, sec 1): 2, 9, 15 (Use the substitution u = (1+e^2x)^1/2, i.e., x = (ln(u²-1))/2.), 18, 33 (See problem 48 on page 481 for a reduction formula for powers of secant.). (Solutions)
• Page 563 (Ch 8, sec 3): 2, 3, 5, 14, 22, 24, 25, 28, 29. (Solutions)

Chapter 10:

• Page 656 (Ch 10, sec 1): 6, 7, 10, 12, 15, 22, 23, 24, 42. (Solutions)
• Page 666 (Ch 10, sec 2): 2, 4, 6, 9 (graph not required), 13, 14, 19, 29, 32, 38, 39, 42. (Challenge: 74. See 73 for a parametrization of part of the boundary.) (Solutions)

Chapter 11:

• Page 710 (Ch 11, sec 1): 4, 5, 10, 11, 13, 17, 20, 23 (an example of a bounded sequence that is not convergent; just list the first 5 values using a calculator), 24, 36, 37, 49, 55, 56, 57, 64 (Explain why the first sentence shows that the sequence is convergent, and find the limit; you need not "Show", i.e., prove, anything.), 65(b). (Solutions)
• Page 720 (Ch 11, sec 2): 9, 16, 18, 21, 27, 28, 42, 43, 52ab (The parenthetical comment in (a) is used in (b), not in (a).), 56 (Solutions); and Page 729 (Ch 11, sec 3): 4, 7, 9, 10, 12, 20, 32. (Solutions)
• Page 748 (Ch 11, sec 7): 1, 5, 6, 7, 8, 9, 16, 22, 24, 31. (Solutions)
• Page 753 (Ch 11, sec 8): 3, 5, 8, 13, 18, 22, 24, 30, 38. (As usual, we are only interested in absolute convergence, so factors of -1 should be ignored.) (Solutions)
• Page 759 (Ch 11, sec 9): 4, 6, 11, 13, 15, 18, 24, 38. (Solutions)
• Page 770 (Ch 11, sec 10): 11, 13, 14, 23, 25, 26, 32, 40, 43, 48, 57, 58, 60. (Solutions)

Chapter 7 (again):

• Page 527 (Ch 7, sec 7): 1, 7, 14, 19, 25, 32, 47. (Solutions)

Chapter 9:

• Page 591 (Ch 9, sec 1): 2, 3, 5, 9, 12, 13, 14 (Solutions); and Page 599 (Ch 9, sec 2): 2a(i,iv only)b, 4, 5, 8 (Here is a blank direction field on which to sketch.), 19, 22. (Solutions)
• Page 607 (Ch 9, sec 3): 2, 5, 8, 11, 12, 16, 19, 21 (not the graph), 33 (the limit as t approaches infinity), 37, 39. (Solutions)