Math 142B Calculus II for Biology -- Homework
Fall 2009

• Papers are always due at the beginning of class.
• Use pencil and eraser rather than ink. Messy papers will not be graded.
• Fold your paper along the long axis, and on the outside write
  • Your full name
  • Math 142
  • HW #
  • Box #

• HW 33 Due Monday, November 23, at 12:30 pm
  • Set up AND evaluate the arclength integral for the curve traced out by x(t) = 3cos(t), y(t) = 3sin(t), where 0 <= t <= pi. Graph the curve.
  • textbook: p. 394: 55, 57, 59, 64
• HW 32 Due Thursday, November 19, at 12:30 pm
  • 1. Change these cartesean coordinates into polar coordinates. (a) (0,5), (b) (-3,4)
  • 2. Change these polar coordinates into cartesian coordinates. (a) (2,pi/6), (b) (-3,0)
  • 3. Change these equations in cartesian coordinates to equations in polar coordinates. (a) y = sqrt(3)*x, (b) x^2 + y^2 = 25, (c) y = x + 1.
• HW 31 Due Wednesday, November 18, at 12:30 pm
  • Handout: p. 610: 11, 23. Also p. 621: 34.
• HW 30 Due Tuesday, November 17, at 12:30 pm
  • Handout: p. 604: 9, 10, 14. Also p. 610: 4, 5
• HW 29 Due Thursday, November 12, at 12:30 pm
  • Find the Taylor polynomial of degree 5 for sinx about x = pi/3.
  • Find the Taylor polynomial of degree 3 for e^(2x-2) about x = 1.
  • Find the radius and interval of convergence. Don't forget to test the endpoints and show all the work.
• HW 28 Due Wednesday, November 11, at 12:30 pm
  • Textbook: p. 469: 6-10
• HW 27 Due Tuesday, November 10, at 12:30 pm
  • Handout: p. 598: 1(a)-(b), 3-5, 19, 24
  • (Please continue in the order listed here.) p. 599: 20-22, 31 [Hint: On #21, note that (-3)^n = ( (-1)*3 )^n = (-1)^n * 3^n.]
• HW 26 Due Thursday, November 5, at 12:30 pm
  • Handout: p. 591: 3-5, 8, 9, 12, 16, 17, 18, 19 (Hints: #12--Split into two series. #17--Try LCT with series 1/3^n, which is geometric. #18--Try regular comparison test, remembering that sin^2(x) <= 1.) Please give yourself time to go by the Math Center if you get stuck. Feel free to email me if you get stuck on a problem.
• HW 25 Due Wednesday, November 4, at 12:30 pm
  • Some series problems
• HW 24 Due Tuesday, November 3, at 12:30 pm
  • HANDOUT, not textbook: p. 580: 1, 2, 9, 11-25, 31, 32, 33, 35
• HW 23 Due Wednesday, October 28, at 12:30 pm
  • p. 99: 29, 31, 32, 45, 46, 49, 53-56
• HW 22 Due Wednesday, October 21, at 12:30 pm
  • p. 99: 2-6, 11-15, 20-26
• HW 21 Due Tuesday, October 20, at 12:30 pm
  • Equilibria and Stability problems
• HW 20 Due Monday, October 19, at 12:30 pm
  • p. 492: 25, 32, 41, 47, 49
• HW 19 Due Wednesday, October 14, at 12:30 pm
  • p. 491: 1-4, 10, 15, 17, 20, 37, 45
• HW 18 Due Wednesday, October 7, at 12:30 pm
  • p. 491: 11, 13 [Show ALL the steps as we did in class. Find the general solution and then the particular solution.]
• HW 17 Due Tuesday, October 6, at 12:30 pm
  • p. 393: 20-24
• HW 16 Due Monday, October 5, at 12:30 pm
  • Disks and Shells problems
• HW 15 Due Wednesday, September 30, at 12:30 pm
  • p. 393: 25-29
• HW 14 Due Tuesday, September 29, at 12:30 pm
  • p. 392: 1, 3, 5, 7, 8
• HW 13 Due Monday, September 28, at 12:30 pm
  • Prove the identity (coshx)^2 - (sinhx)^2 = 1. [Hint: Use the definitions of cosh and sinh.]
  • Prove that the derivative of coshx is sinhx. (Not -sinhx!)
  • Given that exp(it) = cost + isint, prove that sint = (exp(it)-exp(-it))/(2i).
• HW 12 Due Thursday, September 24, at 12:30 pm
  • p. 452: 9-13
  • p. 457: 1-3, 5, 6
• HW 11 Due Wednesday, September 23, at 12:30 pm
  • p. 451: 1-5
• HW 10 Due Tuesday, September 22, at 12:30 pm
  • p. 442: 18-22
• HW 9 Due Wednesday, September 16, at 12:30 pm
  • p. 442: 1, 3, 5, 6, 17
• HW 8 Due Monday, September 14, at 12:30 pm
  • Do all the integrals on the "Integration Summary" handout. Show all work.
• HW 7 Due Thursday, September 10, at 12:30 pm
  • p. 424: 23-32
• HW 6 Due Wednesday, September 9, at 12:30 pm
  • p. 424: 1-3, 5-7, 9-12 [Hint: 1/tan is cos/sin]
• HW 5 Due Thursday, September 3, at 12:30 pm
  • p. 414: 15, 21, 26, 27, 31, 33
• HW 4 Due Wednesday, September 2, at 12:30 pm
  • p. 407: 43, 52, 57
  • p. 414: 1, 6, 7, 8, 10, 11, 19
• HW 3 Due Tuesday, September 1, at 12:30 pm
  • p. 407: 17, 19, 21, 24, 26, 29, 31, 32, 36
  • Find the antiderivative of tanx. (We did cotx at the end of class on Monday.)
• HW 2 Due Monday, August 31, at 12:30 pm
  • p. 406: 1-16
• HW 1 Due Tuesday, August 25, at 12:30 pm
  • p. 371: 8, 9, 22, 23, 31, 32, 37, 38, 41, 42, 99, 100
  • Start studying for Test 1, Thursday 27 August, over derivatives
    1. Derivative Quiz
    2. Derivative Quiz Key
    3. More Derivatives
    4. More Derivatives Key
    5. Dude, you want Even More Derivatives?
    6. Even More Derivatives Key