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(Last modified: Friday, April 18, 2003, 8:46 AM )

I'll use Maple syntax for mathematical notation on this page.
All section and page numbers refer to sections from Ostebee/Zorn, Volume 2, Edition 2.

Due Wednesday 4/2 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 4/2

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?
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 a_k of the sequence 1, 2, 4, 8, 16, 32, . . .

Reminders:

• Begin PS 9.
• Return to working on the project.

Due Friday 4/4 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 4/4

Reading questions:

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?

Due Monday 4/7 at 8am

Section 11.2: Infinite Series, Convergence, and Divergence

• To read: Finish the section and reread through Example 4.
• Be sure to understand: The nth term test.

E-mail Subject Line: Math 104 Your Name 4/7

Reading Questions:
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:

• Bring questions on PS 9.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.

Due Wednesday 4/9 at 8am

Section 11.3: Testing for Convergence; Estimating Limits

• To read: The statements of the Comparison test and Integral test for non-negative series.
• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 4/9

Reading questions:

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

Reminders:

• Begin PS 10.
• Project 2 is due Friday.

Due Friday 4/11 at 8am

Section 11.3 Testing for Convergence; Estimating Limits

• To read: Finish the section
• Be sure to understand: The ratio test

E-mail Subject Line: Math 104 Your Name 4/11

Reading Questions:

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

Due Monday 4/14 at 8am

Section 11.3 Testing for Convergence; Estimating Limits

• To read: Really carefully re-read this section.
• Be sure to understand: How it all fits together; when we can use each test.

No Reading Questions Today

Reminders:

• Bring questions on PS 10.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.

Due Wednesday 4/16 at 8am

Section 11.4 Absolute Convergence; Alternating Series

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

E-mail Subject Line: Math 104 Your Name 4/16

Reading Questions:

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

Reminders:

• Begin PS 11.
• Exam 3 is next Tuesday.

Due Friday 4/18 at 8am

Section 11.4 Absolute Convergence; Alternating Series

• To read: Re-read the section.
• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 4/18

Reading Questions:

1. How close does S₁₀₀ approximate the series sum((-1)^k (1/k), k=0 .. infinity) ? Why?

Due Monday 4/21 at 8am

Bring Questions for Exam 3

No Reading Questions Today!
Reminder:

• PS 11 will not be collected, but it will be covered on the exam.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
• As always, you may have handwritten notes on one side of a standard sheet of paper, and you may begin the exam at 12:30 on Tuesday.

Due Wednesday 4/23 at 8am

Section 11.5 Power Series

• To read: All
• Be sure to understand: Examples 4 and 5.

E-mail Subject Line: Math 104 Your Name 4/23

Reading Questions:

1. How do power series differ from the series we have looked at up to this point?
2. What is the interval of convergence of a power series? Explain in your own words.

• Begin PS 12.

Due Friday 4/25 at 8am

Section 11.5 Power Series

• To read: Reread the section.
• Be sure to understand:

No Reading Questions Today

Due Monday 4/28 at 8am

Section 11.6 Power Series as Functions

• To read: All
• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 4/28

Reading Questions:

Give two good reasons for writing a known function ( such as cos(x) ) as a power series.

Reminders:

• Bring questions on PS 12.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.

Due Wednesday 4/30 at 8am

Section 11.7 Taylor Series

• To read: All
• Be sure to understand: The definition of a Taylor series.

E-mail Subject Line: Math 104 Your Name 4/30

Reading Questions:

1. How does a Taylor series differ from a Taylor polynomial?
2. Why would you ever want to find the Taylor series of a function?

Reminder:

• The take-home portion of your final is due Tuesday May 6 at 2pm; the in class will be Tuesday from 2-5pm.

Due Friday 5/2 at 8am

Section 11.7 Taylor Series

• To read: Re-read the section
• Be sure to understand:

No Reading Questions Today

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