Fall 1999, Math 101

CHAPTER 3

Be sure to check back often, because assignments may change!

Due Monday 10/18 at 9am

Section 3.1: Derivatives of Power Functions and Polynomials

• To read: All. The optional section is (surprise) optional.
• 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: All. Also go back and re-read Free Fall with Resistance and Example 4 in Section 2.1.
• Be sure to understand: Examples 2 and 4 in Section 3.2

E-mail Subject Line: Math 101 Your Name 10/18

1. Let f(x)=x10. What is f ' (x)?
2. What does it mean for the function F to be an antiderivative of f?

Reminder:

• The next midterm is 10/28. It will cover Section 2.3 to Section 3.3. Start planning how and when you'll study for it.

Due Wednesday 10/20 at 9am

Section 3.3: Derivatives of Exponential and Logarithmic Functions

• To read: All, but don't obsess over Calculating the Derivative of bx.
• Be sure to understand: Theorems 5, 6, and 7

E-mail Subject Line: Math 101 Your Name 10/20

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

Reminders:

• PS 6 is due Friday. Do all the problems before class on Wednesday, and bring any questions.
• Your next midterm is 10/28. Make sure you've done allthe assigned problems from Sections 2.3 thru 3.3.

Due Friday 10/22 at 9am

Section 3.4: Derivatives of Trigonometric Functions

• To read: All, although page 213 is optional. Do your best to understand Differentiating the Sine Function before class, so it won't come as a complete shock to you when I discuss it in class!
• Be sure to understand: Examples 1 and 2

E-mail Subject Line: Math 101 Your Name 10/22

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)?

Reminders:

• PS 6 (an individual assignment) is due today at 4pm.
• Start reviewing for Midterm 2. Begin re-doing old HW problems.

Due Monday 10/25 at 9am

Section 3.5: New Derivatives From Old: The Product and Quotient Rules

• Be sure to understand: Theorems 9 and 10; Exhibit B on p 219

E-mail Subject Line: Math 101 Your Name 10/25

Find the derivatives of the following functions. Be sure to justify your answer.
1. f(x)=xsin(x)
2. g(x)=x/sin(x)
3. h(x)=xln(x)-x

Note:
There's a formal proof of the product rule in Appendix H, if you're interested. Reminders:

• Work on the study guide, and continue re-working old HW problems.
• There will probably be a review session Wednesday at 9pm, but check with me.

Due Wednesday 10/27 at 9am

This day is reserved for catching up, practicing differentiation, and/or reviewing graphing of derivatives and functions.

Reminders:

• PS 7 is due Friday. Do it before class and bring questions to class Wednesday.
• Continue working on the study guide and on re-doing old problems. Re-read class notes and the book. Get a feel for the big picture.
• If you plan to use one, begin writing your "cheat sheet". As before, it must be one page, front only, handwritten.

Due Friday 10/29 at 9am

Section 3.6: The Chain Rule

• Be sure to understand: Theorem 11 and Example 3

E-mail Subject Line: Math 101 Your Name 10/29

Find the derivatives of the following functions. Be sure to justify your answer.
1. f(x)=sin(x3)
2. g(x)=(sin(x))3
3. h(x)=e2x

Reminders:

• PS 7 is due today at 4pm. This is a group assignment.

Due Monday 11/1 at 9am

Section 3.6: The Chain Rule

• Be sure to understand: All

E-mail Subject Line: Math 101 Your Name 11/1

Find the derivatives of the following functions. Be sure to justify your answer.
1. f(x)=sin(x)cos(x)
2. g(x)=sin(x)/cos(x)
3. h(x)=sin(cos(x))

Reminders:

• Wednesday will end with a differentiation exam. Know how to differentiate all of our "elementary" functions (polynomials, and exponential, logarithmic, and trigonometric functions), and how to differentiate combinations of these created by sums, products, quotients, and compositions.

Here ends Chapter 3

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

Back to: Precalculus | My Homepage | Math and CS