
Math 104  Calculus II  Reading Assignments
March 1999

Be sure to check back, because this may change during the semester.
(Last modified:
Sunday, March 7, 1999,
10:44 PM )
I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 2.
For March 1
Section 8.1 Introduction to Using the Definite Integral
Section 8.2 Finding Volumes 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.
Email Subject Line : Math 104 3/1 Your Name
Reading Questions :
 Let R be the rectangle formed by the xaxis, the yaxis, and the lines
y=1 and x=3.
What is the shape of the solid formed when R is rotated about the xaxis?
 Let T be the triangle formed by the lines y=x, x=1 and the xaxis.
What is the shape of the solid formed when T is rotated about the xaxis?
For March 3
Sick Day today. No class.
For March 5
Section 8.2 Finding Volumes by Integration
 To read : Reread the section for today
 Be sure to understand : Example 3
Email Subject Line : Math 104 3/3 Your Name
Reading Questions:
Consider the region R bounded by the graphs y=x and y=x^{2}.
(Notice R is in the first quadrant). Set up the integral that gives the volume
of the solid formed when R is rotated about
 the xaxis
 the yaxis
For March 8
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.
Email Subject Line : Math 104 3/8 Your Name
Reading Question :
Use the Fact on page 468 to set up the integral that gives the length of the
curve y=x^{3} from x=1 to x=3.
For March 10
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.
Email Subject Line : Math 104 3/10 Your Name
Reading Questions :
 What are the two ways in which an integral may be improper?
 Explain why int( 1/x^{2}, x=1..infty) is improper. Does the integral converge or diverge?
 Explain why int( 1/x^{2}, x=0..1) is improper. Does the integral converge or diverge?
For March 12
Section 10.2 Detecting Convergence, Estimating Limits
 To read : All
 Be sure to understand :
Example 2 and the statement of Theorem 1
Email Subject Line : Math 104 3/12 Your Name
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 2 for approximating
int( 1/(x^{5} +1), x=1..infty). What are the two types?
March 15  19
Spring Break.
For March 22
Work on Project 2 today. No Reading Assignment.
For March 24
Section 10.3 Improper Integrals and Probability
 To read : All
 Be sure to understand :
The section The Normal Density Function
Email Subject Line : Math 104 3/24 Your Name
Reading Questions :
 What is a probability density function?
 What is the connection between a probability density function
and integration?
For March 26
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.
Email Subject Line : Math 104 3/26 Your Name
Reading Questions :
 Does l'Hopital's Rule apply to lim_{(x > infty)} x^{2} / e^{x} ?
Why or why not?
 Does l'Hopital's Rule apply to lim_{(x > infty)} x^{2} / sin(x) ?
Why or why not?
For March 29
The Big Picture. No reading assignment for today.
For March 31
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.
Email Subject Line : Math 104 3/31 Your Name
Reading Questions :
 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 a_{k} of the sequence
1, 2, 4, 8, 16, 32, . . .
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