Fall 2003 Math 104

October, 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 10/1 at 8am

Section 7.2 Finding Volumes by Integration
Guide to Writing Mathematics

• Be sure to understand: The section Solids of revolution

E-mail Subject Line: Math 104 Your Name 10/1

1. 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?
2. 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?

Reminders:

• Begin PS 4.
• Do the best you can on your draft -- the better the draft, the more useful and specific my suggestions will be.

Due Friday 10/3 at 8am

Section 7.2 Finding Volumes by Integration

Reminders:

• The rough draft of your project is due by 2:00 Friday.

Due Monday 10/6 at 8am

Section 8.1 Integration by Parts(continued)

• Be sure to understand: Theorem 1. Be warned that Examples 8 and 9 can be a little slippery.

E-mail Subject Line: Math 104 Your Name 10/6

1. Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
2. Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).

Reminder:

• 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 4.

Due Wednesday 10/8 at 8am

Section 8.1 Integration by Parts

E-mail Subject Line: Math 104 Your Name 10/8

Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? You do not need to evaluate the integral, but explain your choice.

1. int( x*cos(x), x)
2. int(x*cos(x2),x)

Reminders:

• Begin PS 5.

Due Friday 10/10 at 8am

Antidifferentiation Exam

Reminders:

• Final draft of project is due at 2:30 Friday.

Due Monday 10/13 at 8am

Fall Break!

Due Wednesday 10/15 at 8am

Work on Project 2

Reminders:

• Get back into the swing, continue working on PS 5.

Due Friday 10/17 at 8am

Continue work on Project 2

Reminders:

• You've had more than a week without reading questions, don't get out of the habit -- they begin again Monday!

Due Monday 10/20 at 8am

Section 9.1 Taylor Polynomials

• To read: All, but you can skip the section Trigonometric polynomials: Another nice family.
• Be sure to understand: The statement of Theorem 1, Example 7, adn the definition of the Taylor polynomial.

E-mail Subject Line: Math 104 Your Name 10/20

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

Reminder:

• 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 5.

Due Wednesday 10/22 at 8am

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 10/22

What is the point of Theorem 2? Explain in your own words.
Reminders:
• Begin PS 6.
• Exam 2 is Tuesday 10/28
• Finish designing your work of art -- proposals are due before class Friday.

Due Friday 10/24 at 8am

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

E-mail Subject Line: Math 104 Your Name 10/24

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]?
Reminders:
• Friday is the deadline for receiving full credit on the antidifferentiation exam. You really need antidifferentiation to come easily to you for the exam Tuesday!
• By 8am Friday, e-mail a description of the artwork you're creating for your project (what it is, how big it will be, what it will be made of), and attach to it the Maple file containing the list of functions and the picture of how it looks before it's revolved. If all goes well and I'm on the ball, I'll display them, 'cause it's fun to see what everybody else is doing.

Monday 10/27 at 8am

Questions for Exam 2

Reminder:

• 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, problems from the study guide, or the topic that's causing difficulties.
• PS 6 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 10/29 at 8am

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 10/29

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:

• Begin PS 7
• Keep on working on your project -- make sure you know how to find the volume!

Due Friday 10/31 at 8am

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 10/31

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?

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

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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