  ### Math 104 - Calculus II - Reading Assignments March 1999

Be sure to check back, because this may change during the semester.
(Last modified: Sunday, March 7, 1999, 10:44 PM )

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

### For March 1

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 3/1 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 March 3

Sick Day today. No class.

### For March 5

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 3/3 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 8

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 3/8 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 10

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 3/10 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. 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 12

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 3/12 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?

Spring Break.

### For March 22

Work on Project 2 today. No Reading Assignment.

### For March 24

Section 10.3 Improper Integrals and Probability

• To read : All
• Be sure to understand : The section The Normal Density Function

Email Subject Line : Math 104 3/24 Your Name

Reading Questions :

1. What is a probability density function?
2. What is the connection between a probability density function and integration?

### 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 29

The Big Picture. No reading assignment for today.

### For March 31

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 3/31 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, . . .

Math 104 Home | T. Ratliff's Home

Maintained by Tommy Ratliff, tratliff@wheatonma.edu
Last modified: Sunday, March 7, 1999, 10:44 PM