Reading Assignments - Math 101 - Calculus I
January & February 1997

Be sure to check back often, because the assignments may change.
Last Modified: February 21, 1997

For January 29

Course Policies
Notes on Reading Assignments
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
  • Reading Questions:
    1. Give an example of a function that is defined by a formula.
    2. Give an example of a function that is defined by words, without an explicit formula.
    3. Is the balloon in Example 5 rising or falling at time t=5 minutes? Explain.

For January 31

Section 1.2 Graphs
  • To read: All
  • Be sure to understand: Example 3; Example 4 part 3; Operations with constants
  • Reading Questions:
    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 February 3

Section 1.3 Machine Graphics
  • To read: All
  • Be sure to understand: The Six views of the sine function; Example 1
Section 1.4 What is a Function?
  • To read: All
  • Be sure to understand: The Five Examples; the definition of domain and range of a function
  • Reading Questions:
    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 February 5

Re-read Notes on Reading Assignments

Section 1.5 A Field Guide to Elementary Functions

  • To read: Pages 49-61
  • Be sure to understand: The definition of an exponential function and the definition of a logarithm function.
  • Reading Questions:
    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 February 7

Section 1.5 A Field Guide to Elementary Functions (continued)
  • To read: Pages 61-65
  • Be sure to understand: The sine and cosine function defined as circular functions (pg 62)
  • Reading Questions:
    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 February 10

Writing Guide

Section 1.6 New Functions from Old

  • To read: Through Example 4
  • Be sure to understand: The definition of the composition of two functions.
  • Reading Questions:
    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 3, what is (f o g)(-1) ?

For February 12

Re-read Notes on Reading Assignments

Section 1.6 New Functions from Old (continued)

  • To read: Reread through Example 4
  • Reading Questions:
    1. Use the functions f and g from Example 3. Find (f o g)(0) and (g o f)(0).
    2. Let f(x)=x+2 and let g(x) be any function. How is the graph of g o f related to the graph of g? How is the graph of f o g related to the graph of g?

For February 14

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
  • 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 February 17

Section 2.2 Estimating Derivatives: A Closer Look
  • To read: All
  • Be sure to understand: Examples 1, 4, and 5
  • Reading Questions:
    1. What does the term "locally linear" mean?
    2. Explain why the derivative of f(x)=|x| does not exist at x=0.

For February 19

Re-read Course Policies

Section 2.3 The Geometry of Derivatives

  • To read: All
  • 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
  • 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 February 21

Exam today. No reading assignment.

For February 24

No reading assignment today.

For February 26

Section 2.4 The Geometry of Higher-Order Derivatives
  • To read: All
  • Be sure to understand: The Second Derivative Test
  • Reading Questions:
    Look at the graphs of f, f ', and f ' ' on page 133:
    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 February 28

Section 2.5 Average and Instantaneous Rates: Defining the Derivative
  • To read: Through page 146. Be warnded: This is a hard section!
  • Be sure to understand: Example 1, the Section on page 143 Average Speeds, Instantaneous Speeds, and Limits
  • Reading Questions:
    1. Let f(x)=x^2. 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)=x^2. What is the average rate of change of f from x=1 to x=3?

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