Reading Assignments for Calculus 2
    Fall 2007 Math 104

    October, 2007



    Be sure to check back often, because assignments may change!
    (Last modified: Wednesday, September 26, 2007, 4:24 PM )


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


    Due Monday 10/1 at 9am

    Section 8.1 Integration by Parts(continued)

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

    Reading questions:

    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).


    Due Wednesday 10/3 at 9am

    Section 8.1 Integration by Parts
    Guide to Writing Mathematics

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

    Reading questions:
    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:


    Due Friday 10/5 at 9am (this is really the reading for next Wednesday's class)

    Section 9.1 Taylor Polynomials

    E-mail Subject Line: Math 104 Your Name 10/5

    Reading questions:

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

    Reminder:


    Due Monday 10/08 at 9am

    Fall Break!


    Due Wednesday 10/10 at 9am

    Section 9.1 Taylor Polynomials

    No Reading Questions Today
    (If you didn't do the reading questions for last Friday, do them now.)

    Reminder:


    Due Friday 10/12 at 9am

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

    E-mail Subject Line: Math 104 Your Name 10/12

    Reading Questions:

      What is the point of Theorem 2? Explain in your own words.
    Reminders:


    Due Monday 10/15 at 9am

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

    E-mail Subject Line: Math 104 Your Name 10/15

    Reading Questions:

      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:


    Due Wednesday 10/17 at 9am

    Section 10.1: Improper Integrals: Ideas and Definitions

    E-mail Subject Line: Math 104 Your Name 10/17

    Reading questions:

    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:


    Due Friday 10/19 at 9am

    Section 10.1: Improper Integrals: Ideas and Definitions

    No Reading Questions Today

    Reminders:


    Due Monday 10/22 at 9am

    Section 10.2: Detecting Convergence, Estimating Limits

    E-mail Subject Line: Math 104 Your Name 10/22

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

    Reminders:


    Wednesday 10/26 at 9am

    Questions for Exam 2

    No Reading Questions today

    Reminder:


    Due Friday 10/26 at 9am

    Section 10.2: Detecting Convergence, Estimating Limits

    E-mail Subject Line: Math 104 Your Name 10/26

    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)?
    3. If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?


    Due Monday 10/29 at 9am

    Section 10.2: Detecting Convergence, Estimating Limits

    No Reading Questions Today

    Reminders:


    Due Wednesday 10/31 at 9am

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

    E-mail Subject Line: Math 104 Your Name 10/31

    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?
    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, . . .

    Reminders:


    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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