Math 104 - Calculus II - Reading Assignments - October 2001

Be sure to check back, because this may change during the semester.
(Last modified: Monday, October 1, 2001, 8:21 AM )

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


For October 1

Section 9.1 Integration by Parts

To read : Reread the section

Be sure to understand : Example 8

Email Subject Line : Math 104 10/1 Your Name

Reading Questions : Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Why?

  1. int( x*cos(x), x)
  2. int(x*cos(x2),x)

For October 3 and October 5

No reading assignment for these days.

For October 12

Practice Antidifferentiation. No Reading Assignment.


For October 15

Section 8.1 Introduction to Using the Definite Integral
Section 8.2 Finding Volumes by Integration

To read : All

Be sure to understand : The section from 8.2 on Reassembling Riemann's Loaf and Example 1 from 8.2.

Email Subject Line : Math 104 10/15 Your Name

Reading Questions :

  1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
  2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?

For October 17

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 10/17 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 October 19

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 10/19 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 October 22

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.

Email Subject Line : Math 104 10/22 Your Name

Reading Questions :

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


For October 24

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 10/24 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 October 26

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 10/26 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 October 29

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 10/29 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 October 31

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


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Last modified: Monday, October 1, 2001, 8:21 AM