Spring 2006 Math 104

March, 2006

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 3/1 at 9am

Project 1

Reminder:

• Begin PS 6.

Due Friday 3/3 at 9am

Section 9.1 Taylor Polynomials

• To read: All, although you may skip the section Trigonometric Polynomials: Another nice family.
• Be sure to understand: The statement of Theorem 1, Example 7, and the definition of the Taylor polynomial.

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

Explain the basic idea of the Taylor polynomial for a function f(x) at x=x0 in your own words.

Due Monday 3/6 at 9am

Section 9.1 Taylor Polynomials

• To read: Re-read this section again, trying to fit everything together.

Reminder:

• Come to my office hours, tutoring hours!
• Bring unresolved questions on PS 6 to class Monday.
• The math for project 1 should be finished by Monday evening at the latest.

Due Wednesday 3/8 at 9am

Section 9.2 Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials

• To read: All, but you can skip the section Proving Taylor's theorem.
• Be sure to understand: The statement of Theorem 2 and Examples 2 and 3.

E-mail Subject Line: Math 104 Your Name 3/8

What is the point of Theorem 2? Explain in your own words.
Reminders:
• I'll give you the antidifferentiation exam toward the end of class.
• I urge you to bring me a draft of your project for some suggestions.
• Remember that a blank copy of the check-list should be attached to your project when you turn it in.
• Begin PS 7.

Due Friday 3/10 at 9am

Section 9.2 Taylor's Theorem: Accuracy Guarantees for Taylor Polynomials

E-mail Subject Line: Math 104 Your Name 3/10

Let f(x)=sqrt(x).
1. Find P3(x) for f at the base point x0=64.
2. What can you say about the error committed by using P3(x) as an approx for sqrt(x) on the interval [50,80]?

Monday 3/13 through Friday 3/17

Spring Break!

Due Monday 3/20 at 9am

Section 10.1: Improper Integrals: Ideas and Definitions

• Be sure to understand: The section Convergence and divergence: Formal definitions and Examples 1 - 5.

E-mail Subject Line: Math 104 Your Name 3/20

1. What are the two ways in which an integral may be improper?
2. Explain why int( 1/x2, x=1..infinity) 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?

Reminders:

• Mid-semester reminder -- office hours really are an important part of this course. If you haven't come in for questions yet, make a point of stopping by this week, whether it's to address a problem you wish you'd dealt with weeks ago, something that's confusing you now, a subtle point you'd like resolved, or to discuss how what we're learning connects to something you've learned in another class.
• Exam 2 is Tuesday 3/28
• Bring questions on PS 7 to lab Tuesday.

Due Wednesday 3/22 at 9am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: The statements of Theorems 1 and 2 and Example 4.

E-mail Subject Line: Math 104 Your Name 3/22

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 4 for approximating int( 1/(x5 +1), x=1..infty). What are the two types?

Reminders:

• Begin PS 8

Due Friday 3/24 at 9am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: Example 5.

E-mail Subject Line: Math 104 Your Name 3/24

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:

• Monday is the deadline for receiving full credit on the antidifferentiation exam.

Monday 3/27 at 9am

Questions for Exam 2

Reminder:

• Don't wait to bring all your questions your class on Monday -- we might not have time to get through them all. Bring some to my office hours and/or the tutoring hours.
• PS 8 will not be turned in, but will be covered on this exam.
• As before, you may have an 8 1/2 x 11 handwritten front-only sheet of notes, and you may begin the exam at 12:30.

Due Wednesday 3/29 at 9am

Section 10.2: Detecting Convergence, Estimating Limits

Reminders:

• Begin PS 9

Due Friday 3/31 at 9am

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

• To read: The sections Indeterminate Forms and l'Hopital's rule: finding limits by differentiation that begin on page S-18, and all of Section 11.1.
• Be sure to understand: Indeterminate forms, 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 3/31

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, . . .

Here ends the reading for March
Next, go to the reading for April and May!

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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