Math 104 - Calculus II - Reading Assignments
March 2001

Be sure to check back, because this may change during the semester.
(Last modified: Monday, December 11, 2000, 12:33 PM )

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.

For March 2

Section 8.2 Finding Volumes by Integration

To read : Re-read the section for today

Be sure to understand : Example 3

Email Subject Line : Math 104 3/2 Your Name

Reading Questions : Consider the region R bounded by the graphs y=x and y=x2. (Notice R is in the first quadrant). Set up the integral that gives the volume of the solid formed when R is rotated about

  1. the x-axis
  2. the y-axis

For March 5

Work on Group Project 2. No Reading Assignment.

For March 7

Section 8.3 Arclength

To read : All

Be sure to understand : The statement of the Fact at the bottom of page 468, and Example 2.

Email Subject Line : Math 104 3/7 Your Name

Reading Question:

    Use the Fact on page 468 to set up the integral that gives the length of the curve y=x3 from x=1 to x=3.

For March 9

Work on Group Project 2. No Reading Assignment.

For March 19

Section 10.1 When Is an Integral Improper?

To read : All

Be sure to understand : Examples 1, 2, and 4. The formal definitions of convergence and divergence on pages 523 and 524.

Reading Questions : Since this is the first day back from Spring Break, you don't have to send these in.

  1. What are the two ways in which an integral may be improper?
  2. Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge?
  3. Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge?

For March 21

Section 10.2 Detecting Convergence, Estimating Limits

To read : All

Be sure to understand : Example 2 and the statement of Theorem 1

Email Subject Line : Math 104 3/21 Your Name

Reading Questions :

  1. If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty) converge or diverge? Why?
  2. There are two types of errors that arise in Example 2 for approximating int( 1/(x5 +1), x=1..infty). What are the two types?

For March 23

Section 10.2 Detecting Convergence, Estimating Limits

To read : Reread the section.

Be sure to understand : The statement of Theorem 2.

Email Subject Line : Math 104 3/23 Your Name

Reading Questions : Suppose that 0 < f(x) < g(x).

  1. If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
  2. If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
  3. If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?

For March 26

Section 10.4 l'Hopital's Rule: Comparing Rates

  • To read : All, but you may skip the section on Fine Print: Pointers Toward a Proof. We'll talk about a different justification during class.
  • Be sure to understand : The statement of Theorem 3, l'Hopital's Rule.

Email Subject Line : Math 104 3/26 Your Name

Reading Questions :

  1. Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ? Why or why not?
  2. Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ? Why or why not?

For March 28

Q & A for Exam 2 today. No Reading Assignment.

For March 30

Section 11.1 Sequences and Their Limits

  • To read : Through page 557 and the statements of Theorem 2 and Theorem 3.
  • Be sure to understand : The section of Fine Points on page 553, the statements of Theorems 2 and 3.

Email Subject Line : Math 104 3/30 Your Name

Reading Questions :

  1. Does the following sequence converge or diverge? Be sure to explain your answer.
    1, 3, 5, 7, 9, 11, 13, . . .
  2. Find a symbolic expression for the general term ak of the sequence
    1, -2, 4, -8, 16, -32, . . .


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Last modified: Monday, December 11, 2000, 12:33 PM