 ### Reading Assignments - Math 101 - Calculus I September 1997

Be sure to check back often, because the assignments may change.

#### For September 5

Course Policies
Notes for Students (pg xix in the text)

Section 1.1 Functions, Calculus Style

• To read: Through Example 6
• Be sure to understand: Examples 5 and 6

Email Subject Line: Math 101 9/5 Your Name

1. Give an example of a function that is defined by words, without an explicit formula.
2. Using the function m(x) in Example 4, what is m(2)?
3. Is the balloon in Example 5 rising or falling at time t=4 minutes? Explain.

#### For September 8

Section 1.2 Graphs
• Be sure to understand: Example 3; Example 4 part 3; Operations with constants

Email Subject Line: Math 101 9/8 Your Name

1. Explain why the graph of x^2+y^2=1 in Example 1 is not the graph of a function.
2. For which values of x is the graph in Example 3 increasing? decreasing?
3. How does the graph of f(x)+2 compare with the graph of f(x)? the graph of 2 f(x) to the graph of f(x)?

#### For September 10

Section 1.3 Machine Graphics
• Be sure to understand: The Six views of the sine function; Example 1
Section 1.4 What is a Function?
• Be sure to understand: The Five Examples; the definition of domain and range of a function

Email Subject Line: Math 101 9/10 Your Name

1. Give the domain and range of the function f(x)=x^2.
2. Let g(t) = the world's human population t years C.E. Give the domain and range of g.
3. How can you recognize a periodic function from its graph?

#### For September 12

Section 1.5 A Field Guide to Elementary Functions

• Be sure to understand: The definition of an exponential function and the definition of a logarithm function.

Email Subject Line: Math 101 9/12 Your Name

1. What is the domain of the rational function r(x) = x^2/(x^2-1) in Example 3? Why?
2. Every exponential function f(x)=b^x passes through a common point. What is it? Why?
3. Every logarithmic function g(x)=log_b(x) passes through a common point. What is it? Why?

#### For September 15

Section 1.5 A Field Guide to Elementary Functions (continued)
• Be sure to understand: The sine and cosine function defined as circular functions (pg 62)

Email Subject Line: Math 101 9/15 Your Name

1. What are the domain and range of sin(x)?
2. What are the domain and range of tan(x)?
3. What is the period of the cosine function? How can you tell?

#### For September 17

Section 1.6 New Functions from Old
• To read: Through Example 4
• Be sure to understand: The definition of the composition of two functions.

Email Subject Line: Math 101 9/17 Your Name

1. Let f(x)=x^2 and g(x)=sin(x) . What is (f o g)(x) ?
2. Let f(x)=x^2 and g(x)=sin(x) . What is (g o f)(x) ?
3. In Example 2, explain why (f o g)(-4) is undefined.

#### For September 19

No Reading Assignment today because of the project.

#### For September 22

Section 2.1 Amount Functions and Rate Functions: The Idea of the Derivative
• To read: Through page 100
• Be sure to understand: Pages 94-96 on Rates, Amounts, and Cars: The Prime Example

Email Subject Line: Math 101 9/22 Your Name

Reading Questions: Look at the graphs of P(t) and V(t) on page 95.

1. Is the derivative of P positive or negative at t=5 ?
2. Is the second derivative of P positive or negative at t=5 ?
3. Give a value of t where the derivative of P is zero.

#### For September 24

Section 2.2 Estimating Derivatives: A Closer Look
• Be sure to understand: Examples 1, 4, and 5

Email Subject Line: Math 101 9/24 Your Name

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

#### For September 26

Section 2.3 The Geometry of Derivatives

• Be sure to understand: The Extended Example beginning on page 118; The definitions of stationary point, local maximum and minimum, global maximum and minimum, concave up and concave down; The First Derivative Test

Email Subject Line: Math 101 9/26 Your Name

Reading Questions: Look at the graph of f ' in Example 2:

1. Where does f have stationary points?
2. Where is f increasing?
3. Where is f concave up?

#### For September 29

Section 2.4 The Geometry of Higher-Order Derivatives
• Be sure to understand: The Second Derivative Test

Email Subject Line: Math 101 9/29 Your Name