### Math 102 - Calculus I with Economics Applications Reading Assignments

Be sure to check back, because this may change during the semester.
(Last modified: Tuesday, April 26, 2005, 3:10 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 Friday January 28

Section 1.1 Functions, Calculus Style
Section 1.2 Graphs

To read : The Section How to Use This Book: Notes for Students beginning on page xvii. All of Sections 1.1 and 1.2.

Reading Questions : Let f(x)=x2
1. How is the graph of y=f(x)+3 =x2+3 related to the graph of y=f(x)? Why?
2. How is the graph of y=f(x+3) =(x+3)2 related to the graph of y=f(x)? Why?
3. Which of f(x), f(x)+2, and f(x+2) are even? odd?

### For Monday January 31

Appendix E Algebra of Exponentials and Logarithms
Section 1.3 A Field Guide to Elementary Functions

To read : All of Appendix E, and through the section "Logarithm functions" of Section 1.3. Be sure to understand the definition of the logarithm function base b.

1. How are the functions f(x)=3x and g(x)=log3(x) related?
2. Solve for x in the equation: log2(x) + log2(x3)=12

### For Wednesday February 2

Appendix F Trigonometric Functions
Section 1.3 A Field Guide to Elementary Functions

To read : All of Appendix F and finish Section 1.3. Be sure to understand the definitions of sin(x) and cos(x) in terms of the unit circle.

1. What are the domain and range of sin(x)?
2. What is 120 degrees equal to in radians?
3. What is the period of the cosine function? How can you tell?

### For Friday February 4

Section 1.4 Amount Functions and Rate Functions: The Idea of the Derivative

To read : Through Example 4. Be sure understand the section "Rates, amounts, and cars" beginning on page 36.

Reading Questions : Look at the graphs of P(t) and V(t) in Figure 1 on page 37.
1. Is the derivative of P positive or negative at t=5 ? Explain.
2. Is the second derivative of P positive or negative at t=5 ? Explain.
3. Give a value of t where the derivative of P is zero.

### For Monday February 7

Section 1.5 Estimating Derivatives: A Closer Look

To read : All. Make sure to understand Examples 3 and 4.

1. What does the term "locally linear" mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.

### For Wednesday February 9

Section 1.6 The Geometry of Derivatives

To read : All. Be sure to understand the definition of a stationary point and the difference between local and global maxima and minima.

Reading Questions : Look at the graph of f ' in Example 2:
1. Where does f have stationary points? Why?
2. Where is f increasing? Why?
3. Where is f concave up? Why?

### For Friday February 11

Section 1.7 The Geometry of Higher Order Derivatives

To read : All. Think about why the Second Derivative Test makes sense.

Reading Questions : Use the graphs of f, f ', and f ' ' in Figure 3 on page 67.
1. By looking at the graph of f '', how can you tell where f is concave up and concave down?
2. By looking at the graph of f ', how can you tell where f is concave up and concave down?

### For Monday February 14

Section 2.1 Defining the Derivative

To read : All. We'll talk about the formal defintion of the derivative in detail during class.

1. Let f(x)=x3. Find the slope of the secant line from x=-2 to x=4.
2. For a function f, what does the difference quotient ( f(a+h) - f(a) )/ h measure?
3. Let f(x)=x3. What is the average rate of change of f from x=-2 to x=4?

### For Wednesday February 16

Work on Project 1 today. No Reading Assignment.

### For Friday February 18

Section 2.2 Derivatives of Power Functions and Polynomials

To read : Through Theorem 4 on page 97. Be sure to understand Examples 1 and 2.

1. What is the derivative of f(x)=x3?
2. Let f(x)=x1/3 (i.e. the cube root of x). Use the graph of y=f(x) to explain why f'(x) does not exist at x=0.

### For Monday February 21

The Big Picture before Exam 1. No Reading Assignment for today.

### For Wednesday February 23

Section 2.3 Limits

To read : Through Theorem 6. Be sure to understand Example 4 and the defintions of left-hand and right-hand limits.

1. Let g(x)=(x2 - 9)/(x-3) as in Example 2.
• Is g(x) defined at x=3? Why or why not?
• What is limx->3 g(x) ? Why?
2. Is f(x)=|x| continuous at x=0? Why or why not?

### For Friday February 25

Section 2.4 Using Derivative and Antiderivative Formulas

To read : All. Be sure to understand the definition of an antiderivative and Theorems 8, 9, and 10.

1. Explain in your own words what an antiderivative of a function g(x) is.
2. How many antiderivatives does f(x)=3x2 have? Why?

### For Monday February 28

Section 2.6 Derivatives of Exponential and Logarithmic Functions; Modeling Growth

To read : All. Be sure to understand Theorem 12 and the section "Proof by picture" that follows.

1. What is the 82nd derivative of f(x)=ex?
2. Do exponential functions model compound interest well? Explain.

### For Wednesday March 2

Section 2.7 Derivatives of Trignometric Functions: Modeling Oscillation

To read : All. Be sure to understand the section "Differentiating the sine: an analytic proof".

1. What is limh->0 ( cos(h) - 1) / h?
2. What is limh->0 sin(h) / h?
3. Why do we care about the limits in the first two questions?

### For Friday March 4

Section 3.1 Algebraic Combinations: The Product and Quotient Rules

To read : All. Be sure to understand Examples 3, 4 and 5.

Reading Questions : Explain what is wrong with the following calculations and fix them.
1. f(x)=x2 sin(x).   f'(x)=2x cos(x)
2. g(x)=sin(x) / (x2 + 1).   g'(x) = cos(x) / (2x)

### For Monday March 7

Section 3.2 Composition and the Chain Rule

To read : Through Example 12. We'll consider evidence for why the Chain Rule is true during class.

Reading Questions : Explain what is wrong with the following calculations and fix them.
1. f(x)= sin(x2).   f'(x)=cos(2x)
2. g(x)=( sin(x) )3.   g'(x)=3( cos(x) )2

### For Wednesday March 9

Section 3.2 Composition and the Chain Rule
Reread the section, but no Reading Questions for today.

### For Friday March 11

More fun with differentiation. Review Sections 3.1 and 3.2, but no Reading Assignment.

### For March 14 - 18

Spring Break. Surprisingly, no Reading Assignment.

### For Monday March 21

Section 4.3 Optimization

To read : All. Read Examples 2, 3, and 4 carefully.

1. At which x-values can a continuous function f(x) achieve its maximum or minimum value on a closed interval [a,b]?
2. What is the difference between an objective function and a constraint equation?

### For Wednesday March 23

Differentiation Exam today. No Reading Assignment.

### For Friday March 25

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 Monday March 28

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

### For Wednesday March 30

Work on Project 2. No Reading Assignment.

### For Friday April 1

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 Monday April 4

The Big Picture before Exam 2. No Reading Assignment.

### For Wednesday April 6

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 April 8

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 April 11

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 April 13

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 April 15

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 April 18

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 April 20

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

### For Friday April 22

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.

1. Explain, in your own words, the idea of Riemann sums for approximating integrals.
2. If f(x) is decreasing on [a,b], will Ln underestimate or overestimate the integral of f from a to b? How about Rn?

### For Monday April 25

The Big Picture before Exam 3. No Reading Assignment.

### For Wednesday April 27

Section 5.6 Approximating Sums: The Integral as a Limit
Reread the section, but no Reading Questions for today.

### For Friday April 29

Section 2.5 Differential Equations; Modeling Growth

To read : All.