Fall, 2000 Math 104

October 2000

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

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

Due Monday 10/2 at 8am

Q & A for Exam 1

• To read: Review Sections 5.1-5.4, 7.1-7.3, 3.8, and 6.2. Work on the study guide I gave you. Redo old problem sets.
• Be sure to understand: Everything, better than you did the first time you saw it.

Reminders:

• Bring questions on PS 4 to class Monday. PS 4 is a group assignment.
• While you should always have done the problem set before Monday, it is especially important this week, as two of the three sections covered on the problem set will be covered on the exam. Make sure every member of your group has a photocopy of the problem set, to study from.
• For the exam, you may have a "cheat sheet" . Your cheat sheet must follow these guidelines:
• It must be on 8 1/2 x 11 paper (or smaller)
• There can only be writing on one side of the paper.
• Your notes must be in your handwriting. (No typing, no photocopying, no getting a friend to help you write it.) The handwriting must be on that paper (no photocopying pieces of your notes.)
• The exam is during lab. You may begin taking it at 12:30pm. Don't forget to bring your calculator and your "cheat sheet".

Due Wednesday 10/4 at 8am

Section 9.1: Integration By Parts (continued)

• Be sure to understand: Example 8

E-mail Subject Line: Math 104 Your Name 10/4

Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Why?
1. int( x*cos(x), x)
2. int(x*cos(x2),x)

Reminder:

• Class is in SC B243 Wednesday!
• PS 4 (group) is due Wednesday.
• Look at PS 5.

Due Friday 10/6 at 8am

Practice Antidifferentiating

• Be sure to understand: All

Reminders:

• As we have Fall Break Monday and Tuesday, please begin PS 5 (I know it's been a tough couple of weeks) and bring any questions you have to class Friday.

Due Wednesday 10/11 at 8am

Section 8.1: Introduction To Using the Definite Integral
Section 8.2: Finding Volume By Integration

• Be sure to understand: The section from 8.2 on Reassembling Riemann's Loaf and Example 1 from 8.2.

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

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?

Reminder:

• PS 5 (ind) is due Wednesday.
• Look at PS 6 on the course web page.

Due Friday 10/13 at 8am

Section 8.2: Finding Volumes By Integration

• Be sure to understand: All

E-mail Subject Line: Math 104 Your Name 10/13

Consider the region R bounded by the graphs y=x and y=x2. (Notice R is in the first quadrant). Set up the integral that gives the volume of the solid formed when R is rotated about
1. the x-axis
2. the y-axis

Due Monday 10/16 at 8am

Section 8.3: Arclength

• Be sure to understand: The statement of the Fact at the bottom of page 468, and Example 2.

E-mail Subject Line: Math 104 Your Name 10/16

1. Use the Fact on page 468 to set up the integral that gives the length of the curve y=x3 from x=1 to x=3.

Reminders:

• The Antidifferentiation Exam is on Tuesday during lab. Practice, practice, practice! Go back and do lots of problems from Sections 6.2 and 9.1.
• Bring questions on PS 6 (group) to class on Monday.
• If you have questions, please come to my office hours: that's what they're for!

Due Wednesday 10/18 at 8am

Project 2

• To read: All of it.
• Be sure to understand: What the client is asking you to do!

Reminder:

• PS 6 (group) is due Wednesday.
• If you have last lingering questions, and would like some help in addition to my office hours, e-mail Annie (at amachaff) before 5pm Tuesday, and let her know you'd like to meet with her Tuesday night at 8pm in A102.

Due Friday 10/20 at 8am

Project 2

• To read: What you've done so far. Come up with more ideas.
• Be sure to understand: What you're going to do next!

Reminder:

• If you haven't already passed it, remember to keep taking the antidifferentiation exam until you do! The deadline for getting full credit is 10/27.
• Set aside the evening of November 13th! The first annual Normal Johnson lecture in Mathematics, given by Tom Banchoff will be at 7:30 that evening. It should be a great talk, it will give you a view of another aspect of math, and I am requiring that you attend.

Due Monday 10/23 at 8am

Section 10.1: When Is an Integral Improper?

• Be sure to understand: Examples 1, 2, and 4. The formal definitions of convergence and divergence on pages 523 and 524.

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

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

• Bring questions on PS 7 (ind) to class on Monday.

Due Wednesday 10/25 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: Example 2 and the statement of Theorem 1

E-mail Subject Line: Math 104 Your Name 10/25

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

Reminder:

• PS 7 (ind) is due Wednesday.
• If you have last lingering questions, e-mail Annie by 5pm Tuesday (at amachaff), and let her know you'd like to meet with her at 8pm Tuesday in A102.
• Look at PS 8.
• Don't forget: The deadline for passing the antidifferentiation exam for full credit is Friday!

Due Friday 10/27 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• Be sure to understand: The statement of Theorem 2.

E-mail Subject Line: Math 104 Your Name 10/27

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)?

Reminders:

• Don't forget the deadline for receiving full credit on the antidifferentiation exam is 4pm on Friday. The deadline for getting 70% on it is Tuesday!
• Plan on having the calculations involved in solving your client's problem done by Friday afternoon at the absolute latest, and on bringing a rough draft to me by Friday or Monday.

Due Monday 10/30 at 8am

Section 10.4: l'Hopital's Rule: Comparing Rates

• To read: All, but you may skip the section on Fine Print: Pointers Toward a Proof. We'll talk about a different justification during class.
• Be sure to understand: The statement of Theorem 3, l'Hopital's Rule.

E-mail Subject Line: Math 104 Your Name 10/30

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?

Reminders:

• Bring questions on PS 8 (group) to class on Monday.
• If you missed the deadline for full credit on the antidifferentiation exam, you have until Tuesday (Halloween) to at least get 70% on it.
• Exam 2 is next week, on Tuesday November 7, which is also election day.
• Remember your project is due Wednesday, rather than Friday! Bring rough drafts in to me soon!
• And, as always, f you have any questions, please come to my office hours!

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) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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