Math 104 - Calculus II - Reading Assignments - October 2001

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

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 / e^x ? 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.