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

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

#### For October 1

Exam 1 today. No Reading Assignment.

#### For October 3

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 10/3 Your Name

1. Let f(x)=x2. 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)=x2. What is the average rate of change of f from x=1 to x=3?

#### For October 6

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 10/6 Your Name

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 8

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 10/8 Your Name

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

#### For October 10

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 10/10 Your Name

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?
3. The equation h(t)=-16t2 + v0 t + h0 gives the height of a falling object at time t. What do the constants v0 and h0 measure?

#### For October 15

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

Email Subject Line: Math 101 10/15 Your Name

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 17

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 10/17 Your Name

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 20

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

Email Subject Line: Math 101 10/20 Your Name

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

#### For October 22

Exam 2 today. No Reading Assignment.

#### For October 24

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

Email Subject Line: Math 101 10/24 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 29

Differentiation Exam today. No reading assignment.

#### For October 31

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

Email Subject Line: Math 101 10/31 Your Name

Reading Questions: 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'
3. y(t)=(1/2)et2; y'=ty

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