Fall 2003, Math 104

November, 2003

Be sure to check back often, because assignments may change!

All section and page numbers refer to sections from Ostebee/Zorn, Volume 2, Edition 2.

Due Monday 11/3 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: Example 5.

E-mail Subject Line: Math 104 Your Name 11/3

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)?

Reminders:

• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 7.

Due Wednesday 11/5 at 8am

Section 4.2 More on Limits: Limits Involving Infinity and l'Hopital's Rule
Section 11.1 Sequences and Their Limits

• To read: The section l'Hopital's rule: finding limits by differentiation that begins on page S-19 and all of Section 11.1.
• Be sure to understand: The statement of l'Hopital's rule and the section Terminology and basic examples in Section 11.1.

E-mail Subject Line: Math 104 Your Name 11/5

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

Reminders:

• Project 2 is due Wednesday at 2:30 pm.
• Begin PS 8. (Remember -- work on hw throughout the week!)

Due Friday 11/7 at 8am

Section 4.2 More on Limits: Limits Involving Infinity and l'Hopital's Rule
Section 11.1 Sequences and Their Limits

• To read: Re-read these sections and make sure they make sense to you!

Due Monday 11/10 at 8am

Section 11.2 Infinite Series, Convergence, and Divergence

• To read: Through Example 4. This can be tough going.
• Be sure to understand: The sections Why series matter: A look ahead and Definitions and terminology.

E-mail Subject Line: Math 104 Your Name 11/10

1. There are two sequences associated with every series. What are they?
2. Does the geometric series sum((1/4)k,k=0..infinity) converge or diverge? Why?

Reminders:

• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 8.

Due Wednesday 11/12 at 8am

Section 11.2: Infinite Series, Convergence, and Divergence

• Be sure to understand: The nth term test.

E-mail Subject Line: Math 104 Your Name 11/12

What does the nth Term Test tell you about each series? Explain.

1. sum(sin(k), k=0..infinity)
2. sum(1/k , k=1..infinity)

Reminders:

• Begin PS 9.

Due Friday 11/14 at 8am

Section 11.3: Testing for Convergence; Estimating Limits

• To read: Through the section on the Comparison test.
• Be sure to understand: How to use the comparison test to determine convergence; how to use it to estimate the accuracy of an approximation.

E-mail Subject Line: Math 104 Your Name 11/14

1. Explain in a couple of sentences why the Comparison Test makes sense.

Due Monday 11/17 at 8am

Section 11.3 Testing for Convergence; Estimating Limits

• To read: Through the section on the Integral Test
• Be sure to understand: How to use the Integral test to determine convergence and divergence; how to use the Integral test to approximate to a desired accuracy.

E-mail Subject Line: Math 104 Your Name 11/17

1. Explain in a couple sentences why the Integral Test makes sense.

Reminders:

• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 9.

Due Wednesday 11/19 at 8am

Section 11.3 Testing for Convergence; Estimating Limits

• To read: Finish the section. Go back and re-read the whole thing.
• Be sure to understand: How to use the ratio test to determine convergence and divergence.

E-mail Subject Line: Math 104 Your Name 11/19

1. Explain in a couple of sentences why the Ratio Test makes sense.
Reminders:
• Begin PS 10.
• Exam 3 is next Tuesday.

Due Friday 11/21 at 8am

Section 11.4 Absolute Convergence; Alternating Series

• Be sure to understand: The statements of the Alternating Series test

E-mail Subject Line: Math 104 Your Name 11/21

1. Give an example of a series that is conditionally convergent. Explain.
2. Give an example of a series that is absolutely convergent. Explain.

Reminder:

• Rachel's help session has been moved to Sunday night, 7:30pm-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 4pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, problems from the study guide, or the topic that's causing difficulties.
• PS 10 will not be collected, but it will be covered on the exam. Bring questions on the homework Friday, and we'll go over some of them, to make Monday less frazzled.

Due Monday 11/24 at 8am

Bring Questions for Exam 3

Reminder:

• PS 10 will not be collected, but it will be covered on the exam.
• As always, you may have handwritten notes on one side of a standard sheet of paper.

Here ends the reading for November
Next, go to the reading for December!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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