Math 104 - Calculus II
Reading Assignments - October 2004
Be sure to check back, because this may change during the semester.
(Last modified:
Wednesday, October 20, 2004,
3:33 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2, 2nd Edition.
For Friday October 1
Section 7.3 Work
To read :
All
Be sure to understand :
The section Work as an integral and Examples 2 and 3.
Reading Questions :
- What simplifying assumptions are made in this section? Are these
completely realistic?
- Why do we need to use calculus to calculate work when the force varies?
For Monday October 4
Section 8.1 Integration by Parts
To read :
All
Be sure to understand :
Theorem 1. Be warned that Examples 8 and 9 can be a little slippery.
Reading Questions :
- Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
- Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).
For Wednesday October 6
Section 8.1 Integration by Parts
To read :
Reread the section for today
Reading Questions :
Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Do not evaluate the integral, but explain your choice.
- int( x*cos(x), x)
- int(x*cos(x2),x)
For Friday October 8
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, and the definition of
the Taylor polynomial.
Reading Question :
Explain the basic idea of the Taylor polynomial for a function f(x)
at x=x0 in your own words.
For Monday October 11
Fall Break. No Reading Assignment.
For Wednesday October 13
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.
Reading Questions :
What is the point of Theorem 2? Explain in your own words.
For Friday October 15
Reread the section, but no Reading Questions for today.
For Monday October 18
Section 10.1 Improper Integrals: Ideas and Definitions
To read :
All
Be sure to understand :
The section Convergence and divergence: Formal definitions
and Examples 1 - 5.
Reading Questions :
- What are the two ways in which an integral may be improper?
- Explain why int( 1/x2, x=1..infty) is improper.
- Explain why int( 1/x2, x=0..1) is improper.
For Wednesday October 20
Section 10.2 Detecting Convergence, Estimating Limits
To read :
All
Be sure to understand :
The statements of Theorems 1 and 2 and Example 4.
Reading Questions :
Suppose that 0 < f(x) < g(x).
- If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
- If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
- If int(f(x), x=1. .infty) converges, what can you conclude about int( g(x), x=1. . infty)?
For Friday October 22
Section 10.2 Detecting Convergence, Estimating Limits
To read :
Reread the section for today.
Be sure to understand :
Example 5.
Reading Questions :
- 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?
- There are two types of errors that arise in Example 4 for approximating
int( 1/(x5 +1), x=1..infty). What are the sources of these errors?
For Monday October 25
Reread the section, but no Reading Questions for today.
For Wednesday October 27
The Big Picture before Exam 2. No Reading Assignment for today.
For Friday October 29
Section 4.2 More on Limits: Limits Involving Infinity and l'Hopital's Rule
Section 11.1 Sequences and Their Limits
To read :
The section l'Hopital's rule: finding limits by differentiation
that begins on page S-19 and all of Section 11.1.
Be sure to understand :
The statement of l'Hopital's rule and the section Terminology and basic examples in Section 11.1.
Reading Questions :
- Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ?
Why or why not?
- Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ?
Why or why not?
- Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
- Find a symbolic expression for the general term ak of the sequence
1, 2, 4, 8, 16, 32, . . .
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