Reading Assignments -
Math 104 - Calculus II
October 1997
I'll use Maple syntax for mathematical notation on this page.
Be sure to check back often, because the assignments may change.
For October 1
Reread Section 9.1 Integration by Parts from last Friday, (September 26).
Since you had the exam on Monday, there are no reading questions for today.
For October3
Section 8.1 Introduction to Using the Definite Integral
- To read: All
- Be sure to understand: The section
Two Views of the Definite Integral
Email Subject Line: Math 104 10/3 Your Name
Reading Questions:
- What are two different interpretations of the definite integral int( f(x), x=a..b) ?
- Do these same interpretations apply to an indefinite integral? Why or why not?
For October 6
Antidifferentiation Exam today. No Reading Assignment.
For October 8
Section 8.2 Finding Volumes by Integration
- To read: All
- Be sure to understand:
The section on Reassembling Riemann's Loaf and Example 1
Email Subject Line: Math 104 10/8 Your Name
Reading Questions:
- 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?
- 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 10
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.
We'll talk about the section How Long is C_{n}? in class.
Email Subject Line: Math 104 10/10 Your Name
Reading Question:
- Use the Fact on page 468 to set up the integral that gives the length of the
curve y=x^{3} from x=1 to x=3.
For October 13
Fall Break. No Reading Assignment, of course.
For October 15
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 10/17 Your Name
Reading Questions: Since this is the first day after Fall Break, you don't have to send these in.
- What are the two ways in which an integral may be improper?
- Explain why int( 1/x^2, x=1..infty) is improper. Does the integral converge or diverge?
- Explain why int( 1/x^2, x=0..1) is improper. Does the integral converge or diverge?
For October 17
Work on Project 2 today. No Reading Assignment.
For October 20
Section 10.2 Detecting Convergence, Estimating Limits
- To read: Through Example 5
- Be sure to understand:
Example 2 and the statement of Theorem 1
Email Subject Line: Math 104 10/20 Your Name
Reading Questions:
- 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?
- There are two types of errors that arise in Example 2 for approximating
int( 1/(x^5 +1), x=1..infty). What are the two types?
For October 22
Section 10.2 Detecting Convergence, Estimating Limits (continued)
- To read: The remainder of the section.
- Be sure to understand:
The statement of Theorem 2
Email Subject Line: Math 104 10/22 Your Name
Reading Question:
- Does int( cos(x)/x^2, x=1. .infty) converge or diverge? Why?
For October 24
Section 10.3 Improper Integrals and Probability
- To read: Through page 539
- Be sure to understand:
The definition of a probability density function, Example 1
Email Subject Line: Math 104 10/24 Your Name
Reading Questions:
- What does the mean of a probability density function measure?
- What does the standard deviaion of a probability density function measure?
For October 27
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 10/27 Your Name
Reading Questions:
- Does l'Hopital's Rule apply to lim_{(x -> infty)} x^{2} / e^{x} ?
Why or why not?
- Does l'Hopital's Rule apply to lim_{(x -> infty)} x^{2} / sin(x) ?
Why or why not?
For October 29
Section 11.1 Sequences and Their Limits
- To read: All
- Be sure to understand:
The section of Fine Points on page 553, the statement of Theorem 3.
Email Subject Line: Math 104 10/29 Your Name
Reading Questions:
- Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
- What is a monotone sequence?
For October 31
Exam 2 today. No Reading Assignment.
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