### Math 102 - Calculus I with Economics Applications Reading Assignments - November & December 2003

Be sure to check back, because this may change during the semester.
(Last modified: Sunday, August 17, 2003, 2:11 PM )

I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition by Ostebee/Zorn.

### For Monday November 3

Section 4.7 Building Polynomials to Order: Taylor Polynomials

To read : All. Be sure to understand Examples 5 and 8.

1. Why would you want to find the Taylor polynomial of a function?
2. In your own words, briefly explain the idea of building the Taylor polynomial for a function f(x).

### For Wednesday November 5

The Big Picture before Exam 2. No Reading Assignment.

### For Friday November 7

Section 4.7 Building Polynomials to Order: Taylor Polynomials
Reread the section, but no Reading Questions for today.

### For Monday November 10

Section 4.8 Why Continuity Matters

To read : All. Be sure to understand the statement of the Intermediate Value Theorem.

1. What are the hypotheses of the Intermediate Value Theorem?
2. What is the conclusion of the Intermediate Value Theorem?

### For Wednesday November 12

Section 4.9 Why Differentiability Matters: The Mean Value Theorem

To read : All. Be sure to understand the statement of the Mean Value Theorem and the section "What the MVT says".

1. What are the hypotheses of the Mean Value Theorem?
2. What is the conclusion of the Mean Value Theorem?
3. Explain the MVT using "car talk" (that is, using velocity).

### For Friday November 14

Section 5.1 Areas and Integrals

To read : All. Be sure to understand the definition of the integral, Example 2, and the section "Properties of the integral" beginning on page 306.

1. What does the integral of a function f from x=a to x=b measure?
2. Is the integral of f(x)=5x from x=-1 to x=3 positive or negative? Why?

### For Monday November 17

Section 5.2 The Area Function

To read : All. Be sure to understand the definition of the area function and Examples 2, 3, and 4.

1. Let f be any function. What does the area function Af(x) measure?
2. Let f(t)=t and let a=0. What is Af(1)?

### For Wednesday November 19

Section 5.3 The Fundamental Theorem of Calculus

To read : All, but you can skip the proof of the FTC in the section. We'll look at a different approach in class.

1. Find the area between the x-axis and the graph of f(x)=x3 + 4 from x=0 to x=3.
2. Does every continuous function have an antiderivative? Why or why not?

### For Friday November 21

Section 5.3 The Fundamental Theorem of Calculus

To read : Re-read the section for today.

1. If f(x)=3x-5 and a=2, where is Af increasing? decreasing? Why?
2. How would your answer change if a=0?

### For Monday November 24

Section 5.4 Finding Antiderivatives: The Method of Substitution

To read : All. Be sure to understand Examples 8, 9, and 10.

1. Explain the difference between a definite integral and an indefinite integral.
2. What are the three steps in the process of substitution?
3. Substitution attempts to undo one of the techniques of differentiation. Which one is it?

### For Wednesday November 26 & Friday November 28

Thanksgiving Break.

### For Monday December 1

Section 5.4 Finding Antiderivatives: The Method of Substitution Reread the section, but no Reading Questions for today.

### For Wednesday December 3

The Big Picture before Exam 3. No Reading Assignment.

### For Friday December 5

Section 5.6 Approximating Sums: The Integral as a Limit

To read : All. Be sure to understand the definition of a Riemann sum and Example 3.