For November 3

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 11/3 Your Name

Reading Question:

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

For November 5

For November 7

Section 4.6 Optimization

• To read: Through Example 5
• Be sure to understand: The discussion on pages 297-298 begining with Local vs. Global Extreme Values and continuing through Example 3

Email Subject Line: Math 101 11/7 Your Name

Reading Questions:

1. What is the difference between a critical point of f and a stationary point of f?
2. Where can the maximum and minimum values of continuous function occur on a closed interval?

For November 10

Section 4.10 Why Continuity Matters

• To read: All
• Be sure to understand: The statement of the Intermediate Value Theorem, Example 2

Email Subject Line: Math 101 11/10 Your Name

Reading Questions:

1. What are the hypotheses of the Intermediate Value Theorem?
2. What is the conclusion of the Intermediate Value Theorem?

For November 12

Section 4.11 Why Differentiability Matters: The Mean Value Theorem

• To read: Through page 334
• Be sure to understand: The statement of the Mean Value Theorem; the section What the MVT Says on page 333; Question 1 and Theorem 9 on page 334

Email Subject Line: Math 101 11/12 Your Name

Reading Questions:

1. What are the hypotheses of the Mean Value Theorem?
2. What is the conclusion of the Mean Value Theorem?
3. Explain the MVT using "car talk" (that is, using velocity).

For November 14

No Reading Assignment today.

For November 17

Section 5.1: Areas and Integrals

• To read: Pages 341-349
• Be sure to understand: The definition of the integral on page 342; Example 2; the section Properties of the Integral beginning on page 345

Email Subject Line: Math 101 11/17 Your Name

Reading Questions:

1. What does the integral of a function f from x=a to x=b measure?
2. Is the integral of f(x)=5x from x=0 to x=3 positive or negative?

For November19

Re-read pages 341-349 of Section 5.1.

Email Subject Line: Math 101 11/19 Your Name

Reading Question:

Is the integral of f(x)=5x from x=-1 to x=3 positive or negative? Why?

For November 21

For November24

Section 5.2: The Area Function

• To read: All
• Be sure to understand: The definition of the Area Function on page 357; Examples 1 and 2

Email Subject Line: Math 101 11/24 Your Name

Reading Questions:

1. Let f be any function. What does the area function A_f(x) measure?
2. Let f(t)=t and let a=0. What is A_f(1)?

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