Reading Assignments for Calculus 2
Spring 2002 Math 104

March, 2002

Be sure to check back often, because assignments may change!
Last modified: March 28, 2002

I'll use Maple syntax for mathematical notation on this page.
All section and page numbers refer to sections from Ostebee/Zorn, Vol 2.

Due Friday 3/1 at 8am

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

• To read: All
• 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 3/1

Reading questions:

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:

• If you haven't been coming to my office hours, make the time to stop by!

Due Monday 3/4 at 8am

Section 8.2: Finding Volumes By Integration

• To read: Re-read the section for Friday
• Be sure to understand: All

E-mail Subject Line: Math 104 Your Name 3/4

Reading questions:

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

Reminder:

• Bring remaining questions on PS 5 to class Monday.
• If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.
• Remember the bureacracy concerning group homework:
• The primary author should switch each week.
• Mark the primary author by putting a star by their name.
• Make sure each member of the group has a photocopy of the problem set.
• Groups may not consist of more than 3 people.
• 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 3/6 at 8am

Section 8.3: Arclength

• To read: All
• 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 3/6

Reading Questions:

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:

• Look at PS 6 on the course web page.

Due Friday 3/8 at 8am

The Big Picture

• To read: Re-read Sections 8.1, 8.2, and 8.3.

No reading questions today

Reminders:

• You do have a reading assignment due the Monday after spring break; you may want to get ahead!

Due Monday 3/18 at 8am

Section 10.1: When Is an Integral Improper?

• To read: All
• 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 3/18

Reading questions:

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 remaining questions on PS 6 to class on Monday.
• If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.

Due Wednesday 3/20 at 8am

Project 2

• To read: Have read all of it by Tuesday.
• Be sure to understand: What the client is asking you to do!

No Reading Questions Today!
Reminder:

• Look at PS 7.

Due Friday 3/22 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

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

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

Reading questions:

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:

• Bring questions to my office hours, as always.
• Keep on working on the project!
• Don't forget: The deadline for passing the antidifferentiation exam for full credit is Tuesday!

Due Monday 3/25 at 8am

Section 10.2: Detecting Convergence, Estimating Limits

• To read: Reread the section.
• Be sure to understand: The statement of Theorem 2.

E-mail Subject Line: Math 104 Your Name 3/25

Reading Questions:

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:

• Bring remaining questions on PS 7 to class Monday.
• If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.
• As always, remember the bureacracy regarding group problem sets: switch authors, note the author, photocopy.
• Don't forget the deadline for receiving full credit on the antidifferentiation exam is 4pm on Tuesday. The deadline for getting 80% on it is Monday April 1st!
• Plan on having the calculations involved in solving your client's problem done by Monday morning at the absolute latest, and on bringing a rough draft to me Tuesday or Wednesday.

Due Wednesday 3/27 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 3/27

Reading Questions:

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:

• Look at PS 8.
• Exam 2 is next Tuesday. Make a study plan, and again allow at least 8 hours (even if it turned out you didn't need that long last time -- the material just keeps getting more complicated!).
• The rough draft of your project should be well underway by Wednesday.

Friday 3/29 at 8am

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

No Reading Questions today (unless you never did the reading questions for Wednesday, in which case you should send those on in for half credit!)

Reminder:

• The time and day of the help session has been changed to Sunday at 6:30pm.
• If you missed the deadline for full credit on the antidifferentiation exam, you have until Monday (April Fools) to at least get 80% on it.
• Remember to make the time to come to my office hours!
• Project 2 is due Friday at 3pm. Once again, I urge you to bring in a rough draft beforehand, and to have a friend who is not in this class (and preferably, who is not familiar with Calc 2) read through your letter to see whether they can understand the situation, and whether they find your solution convincing, not confusing, and not too dry.
• Get a start on studying for that exam!

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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