Math 101 - Calculus I - Reading Assignments
October 1998

Be sure to check back, because this may change during the semester.
(Last modified: Wednesday, October 14, 1998, 11:02 AM )

I'll use Maple syntax for mathematical notation on this page.
All numbers indicate sections from Ostebee/Zorn, Vol 1.

For October 1

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

Email Subject Line : Math 101 10/1 Your Name

Reading Questions : Use 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 October 2

Section 2.5 Average and Instantaneous Rates: Defining the Derivative
  • To read: All. Be warned: This is a hard section!
  • Be sure to understand: Example 1, the Section on page 143 Average Speeds, Instantaneous Speeds, and Limits, and the formal definition of the derivative

Email Subject Line: Math 101 10/2 Your Name

Reading Questions:

  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 October 5

Section 2.6 Limits and Continuity
  • To read: All, but you may skip the formal definition of the limit on page 155.
  • Be sure to understand: The connection between Examples 2 and 3; the definition of continuity on page 157

Email Subject Line: Math 101 10/5 Your Name

Reading Questions:

  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 n(x) in Example 8 continuous at x= -3? Why or why not?

For October 7

Section 2.7 Limits Involving Infinity; New Limits from Old
  • To read: All, but you may skip Examples 4, 5, 7 and the Squeeze Principle
  • Be sure to understand: Examples 1 and 3; the section Finding Limis Graphically and Numerically

Email Subject Line: Math 101 10/7 Your Name

Reading Questions: Find the following limits: Explain your answers.

  1. limx->infinity 1/x3
  2. limx->0+ 1/x3
  3. limx->infinity cos(x)

For October 9

Section 3.1 Derivatives of Power Functions and Polynomials
  • To read: All except for the Optional Section on pages 190-191
  • Be sure to understand: Examples 1 and 2; Theorems 1, 2, and 3; the definition of an antiderivative
Section 3.2 Using Derivative and Antiderivative Formulas
  • To read: The section Modeling Motion: Acceleration, Velocity, and Positions plus Example 4 from Section 2.1
  • Be sure to understand: Example 2

Email Subject Line: Math 101 10/9 Your Name

Reading Questions:

  1. Let f(x)=x2. What is f'(x)?
  2. What does it mean for the function F to be an antiderivative of the function f?

For October 12

Fall Break. No Reading Assignment.

For October 14

Section 3.3 Derivatives of Exponential and Logarithm Functions
  • To read: All, but you may skip the section on Calculating the Derivative of bx. We'll discuss this in class.
  • Be sure to understand: Theorems 5, 6, and 7

Reading Questions: Since this is the first day after Fall Break, you don't have to send these in, but you should think about them.

  1. Find an antiderivative for f(x)=ex.
  2. What is the derivative of g(x)=ln(x)?
  3. What is the slope of the line tangent to y=ex at the point (0,1)?

For October 16

Section 3.4 Derivatives of Trigonometric Functions
  • To read: All, but you may skim the subsection "Differentiating the Sine Function" (we'll talk about this in more detail in class) and you may skip page 213.
  • Be sure to understand: Examples 1 and 2

Email Subject Line: Math 101 10/16 Your Name

Reading Questions:

  1. What is limh->0 ( cos(h) - 1) / h?
  2. What is limh->0 sin(h) / h?
  3. Let f(x)=sin(x) + cos(x). What is f'(x)?

For October 19

Section 3.5 New Derivatives from Old: The Product and Quotient Rules
  • To read: All
  • Be sure to understand: Theorems 9 and 10, and Exhibit B, pg 219

Email Subject Line: Math 101 10/19 Your Name

Reading Questions: Find the derivatives of the following functions. Be sure to justify your answer.

  1. f(x) = x sin(x)
  2. g(x) = x / sin(x)
  3. h(x) = x ln(x) - x

For October 21

Exam 2 today. No Reading Assignment.

For October 23

Section 3.6 New Derivatives from Old: The Chain Rule
  • To read: All
  • Be sure to understand: Theorem 11 and Example 3

Email Subject Line: Math 101 10/23 Your Name

Reading Questions: Find the derivatives of the following functions:

  1. f(x) = sin(x3)
  2. g(x) = ( sin(x) )3
  3. h(x) = e2x

For October 26

Reread Section 3.6. No Reading Questions to email today.

For October 28

Section 4.1 Differential Equations and Their Solutions
  • To read: All.
  • Be sure to understand: Examples 3 and 6.

Reading Questions: Because of the Differentiation Exam, you don't have to send these in, but you should think about them.

Decide whether the function y(t) is a solution to the differential equation.

  1. y(t)=sin(t); -y=y''
  2. y(t)=e2t; y=y'

For October 30

Section 4.2 More Differential Equations: Modeling Growth
  • To read: Theorem 1 on page 256, the sections on Radioactive Decay and Biological Populations on pages 259-260, and the Afterword: Discrete versus Continous Growth beginning on page 264
  • Be sure to understand: The statement of Theorem 1 and Examples 3 and 4

Email Subject Line: Math 101 10/30 Your Name

Reading Question:

    Find a solution to the Initial Value Problem y'=3y and y(0)=30 and check your answer by differentiation.


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Last modified: Wednesday, October 14, 1998, 11:02 AM