Math 102  Calculus I with Economics Applications
Reading Assignments  September 2003
Be sure to check back, because this may change during the semester.
(Last modified:
Sunday, August 17, 2003,
1:50 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 September 5
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)=x^{2}
 How is the graph of y=f(x)+3 =x^{2}+3 related to the graph of y=f(x)? Why?
 How is the graph of y=f(x+3) =(x+3)^{2} related to the graph of y=f(x)? Why?
 Which of f(x), f(x)+2, and f(x+2) are even? odd?
For Monday September 8
Section 1.3 A Field Guide to Elementary Functions
To read : All. Be sure to understand the definition of the logarithm
function base b and the definitions of sin(x) and cos(x) in terms of the unit circle.
Reading Questions :
 How are the functions f(x)=3^{x} and g(x)=log_{3}(x) related?
 What are some of the main properties of sin(x)?
For Wednesday September 10
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.
 Is the derivative of P positive or negative at t=5 ? Explain.
 Is the second derivative of P positive or negative at t=5 ? Explain.
 Give a value of t where the derivative of P is zero.
For Friday September 12
Section 1.5 Estimating Derivatives: A Closer Look
To read : All. Make sure to understand Examples 3 and 4.
Reading Questions :
 What does the term "locally linear" mean?
 Explain why the derivative of f(x)=x does not exist at x=0.
For Monday September 15
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:
 Where does f have stationary points? Why?
 Where is f increasing? Why?
 Where is f concave up? Why?
For Wednesday September 17
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.
 By looking at the graph of f '', how can you tell where f is concave up and concave down?
 By looking at the graph of f ', how can you tell where f is concave up and concave down?
For Friday September 19
Work on Project 1 today. No Reading Assignment.
For Monday September 22
Section 1.7 The Geometry of Higher Order Derivatives
Reread the section for today. No Reading Questions.
For Wednesday September 24
Section 2.1 Defining the Derivative
To read : All. We'll talk about the formal defintion of the
derivative in detail during class.
Reading Questions :
 Let f(x)=x^{3}. Find the slope of the secant line from x=2 to x=4.
 For a function f, what does the difference quotient
( f(a+h)  f(a) )/ h measure?
 Let f(x)=x^{3}. What is the average rate of change of f
from x=2 to x=4?
For Friday September 26
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.
Reading Questions :
 What is the derivative of f(x)=x^{3}?
 Let f(x)=x^{1/3} (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 September 29
Section 2.3 Limits
To read : Through Theorem 6. Be sure to understand Example 4
and the defintions of lefthand and righthand limits.
Reading Questions :
 Let g(x)=(x^{2}  9)/(x3) as in Example 2.
 Is g(x) defined at x=3? Why or why not?
 What is lim_{x>3} g(x) ? Why?
 Is f(x)=x continuous at x=0? Why or why not?
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