Spring, 2000 Math 104

March 2000

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

Due Wednesday 3/1 at 8am

Practice Antidifferentiating

• Be sure to understand: All

Reminders:

• Bring questions on PS 5 (ind) to class on Wednesday.
• If you have questions, come to office hours or e-mail Annie at amachaff and arrange to meet her at 9pm in A102 on Thursday evening.

Due Friday 3/3 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 3/3

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 Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.

Due Monday 3/6 at 8am

Section 8.2: Finding Volumes By Integration

• Be sure to understand: All

E-mail Subject Line: Math 104 Your Name 3/6

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

Reminders:

• Look at PS 6 on the course web page.
• 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.

Due Wednesday 3/8 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 3/8

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:

• Bring questions on PS 6 (group) to class on Wednesday.
• If you have questions, come to office hours or e-mail Annie at amachaff and arrange to meet her at 9pm in A102 on Thursday evening.

Due Friday 3/10 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 3/10

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?

Note: This is the reading for the material we'll be covering the Monday after spring break.

Reminder:

• PS 6 (group) is due Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.

Due Monday 3/20 at 8am

Section 10.1: When Is an Integral Improper?

• Be sure to understand: All

Reminders:

• Look at PS 7 on the course web page.
• Don't forget to re-take the antidifferentiation exam until you pass it. The deadline for receiving full credit is 4pm on March 28th.

Due Wednesday 3/22 at 8am

Project 2 (continued)

• To read: Make sure you have read Project 2 before lab on Tuesday.
• Be sure to understand: What the client is asking you to do!

Reminders:

• Bring questions on PS 7 (ind) to class on Wednesday.
• If you have questions, come to office hours or e-mail Annie at amachaff and arrange to meet her at 9pm in A102 on Thursday evening.

Due Friday 3/24 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 3/24

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 Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.
• Try to have the calculations involved in solving your client's problem done by Friday afternoon. Plan on bringing a rough draft to me by Monday or Tuesday.
• Don't forget: The deadline for passing the antidifferentiation exam is Tuesday!

Due Monday 3/27 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 3/27

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:

• Look at PS 8 on the course web page.
• Don't forget the deadline for receiving full credit on the antidifferentiation exam is 4pm on Tuesday.
• Begin writing a rough draft of your response to your client. Remember to use the writing guide and the checklist to guide your composition.
• Exam 2 is next week, on Tuesday April 4th.

Due Wednesday 3/29 at 8am

Section 10.4: l'Hopital's Rule: Comparing Rates (continued)

• 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 3/29

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 Wednesday.
• If you have questions, come to office hours or e-mail Annie at amachaffand arrange to meet her at 9pm in A102 on Thursday evening.

Due Friday 3/31 at 8am

Section 11.1: Sequences and Their Limits

• To read: Through page 557 and the statements of Theorem 2 and Theorem 3.
• Be sure to understand: The section of Fine Points on page 553, the statements of Theorems 2 and 3.

E-mail Subject Line: Math 104 Your Name 3/31

1. Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
2. Find a symbolic expression for the general term ak of the sequence
1, -2, 4, -8, 16, -32, . . .

Reminder:

• PS 8 (group) is due Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.
• Project 2 is also due Friday.
• You may have a "cheat sheet" for the Exam Tuesday.

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

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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