Spring 2003, Math 104

April and May, 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 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

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:

• Begin PS 9.

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

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

• Be sure to understand: The nth term test.

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

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

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

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

• Be sure to understand: How it all fits together; when we can use each test.

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

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

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

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

• Be sure to understand:

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

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

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

• Be sure to understand: Examples 4 and 5.

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

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.
Reminder:
• Begin PS 12.

Due Friday 4/25 at 8am

Section 11.5 Power Series

• Be sure to understand:

Due Monday 4/28 at 8am

Section 11.6 Power Series as Functions

• Be sure to understand:

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

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

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

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

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

• Be sure to understand: