Fall 1999, Math 101

CHAPTER 2

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

Due Monday 9/27 at 9am

A Guide to Writing in a Mathematics Class

Appendices E, F, and G: These are background on Exponentials, Logarithms, and Trig functions. I've mentioned them in class, but I wanted to make it more formal.

Section 2.1: Amount Functions and Rate Functions: The Idea of the Derivative

• To read: Through page 103
• Be sure to understand: pages 94-96 on Rates, Amounts, and Cars; page 98-99 on The Slope of a Graph at a Point: Tangent Lines
• Skim, but don't obsess over: The Racetrack Principle

E-mail Subject Line: Math 101 Your Name 9/27

Look at the graphs of P(t) and V(t) on page 95
1. Is the derivative of P positive or negative at t=5? Explain.
2. Is the second derivative of P positive or negative at t=5? Explain.
3. Give a value of t where the derivative of P is zero.
4. Give a value of t where the second derivative of P is zero.

Reminders:

• PS 3 (due Friday) is a group assignment.
• I love to have visitors to my office hours, so please bring questions to me!

Due Wednesday 9/29 at 9am

Section 2.2: Estimating Derivatives: A Closer Look

• Be sure to understand: Examples 1, 4, and 5

E-mail Subject Line: Math 101 Your Name 9/29

1. What does the term "locally linear" mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.

Reminder:

• Bring lingering questions to class on Wednesday.

Due Friday 10/1 at 9am

Section 2.3: The Geometry of Derivatives

• Be sure to understand: The extended example beginning on page 118; the definitions of stationary point, local maximum and minimum, global maximum and mininum, concave up and concave down; the first derivative test.

E-mail Subject Line: Math 101 Your Name 10/1

Look at the graph of f' in Example 2:
1. Where does f have stationary points?
2. Where is f increasing?
3. Where is f concave up?

Reminder:

• PS 3 is due at 4pm. If you have any last questions, come to my office hours, or to Annie's (remember to e-mail her at amachaff).
• Midterm 1 is 10/7. It will cover thru part of Section 2.3.
• Allow 8-10 hours for studying for this exam. Begin reviewing now. In an ideal world, reviewing consists of:
1. Re-reading all of the text, and your notes, taking notes on the main points and definitions, and looking for connections, relationships, and the big picture.
2. Some people find it valuable to recopy class notes.
3. Redoing as many assigned problems as possible, and trying some I didn't assign.
4. Doing problems from the review at the end of each chapter.
5. Doing the study guide that I'll be handing out.
• For Friday, I suggest you begin studying by making sure you've done every assigned problem, rather than only those I collect, and re-reading all of the text, taking notes on the main points.
• I will give more study hints in the next reading assignment, so don't wait to read them until Monday morning!

Due Monday 10/4 at 9am

Section 2.4

• Be sure to understand: The second derivative test

E-mail Subject Line: Math 101 Your Name 10/4

Use the graphs of f, f', 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 th egraph of f', how can you tell where f is concave up and concave down?

Note:
The relationships exhibited in the reading questions should not be memorized. If you understand them, you can reproduce them at any time, and you're unlikely to make the silly mistakes that can happen when you memorize.

Reminders:

• Keep on studying: Do as many problems as possible. Don't simply look back at old problem sets; save that for when you're stuck. Make a note of those you have difficulty with, then come look at my solutions on Monday.
• I'm probably having a review session. If I haven't announced it in class, ask me about it.

Due Wednesday 10/6 at 9am

Section 2.5: Average and Instantaneous Rates: Defining the Derivative

• To read: All. Be warned: this is a hard section! Read it a few times, of course.
• Be sure to understand: Example 1; page 43: Average Speeds, Instantaneous Speeds, and Limits; the formal definition of the derivative.

New Note: As of today, 10/5, there is a change in plans. We will not talk about this section (2.5) until Friday's class. However, I don't want to assign reading over Fall Break. So I'll assign the reading on Section 2.6 for either Friday or Wednesday, and you can do it whenever fits your schedule better.

E-mail Subject Line: Math 101 Your Name 10/6

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 (again). What is the average rate of change of f from x=-2 to x=4?

Reminders:

• Midterm 1 is Thursday during lab. You may come at 12:30, if you want to begin early.
• Do the study guide that I handed out to you.
• Remember to bring a "cheat sheet", if you want one. It must be 8 1/2 x 11 (or smaller), front only, and handwritten (by you).
• While you do not have to turn in any problems on Friday, you do need to have the new problem set done by the time of the exam, particularly those from Section 2.2 and 2.3. Bring any questions on these problems to class on Wednesday.

Due Friday 10/8 at 9am

Notice: This reading assignment really isn't due until Wednesday the 13th. Depending on your plans for break, you may want to do it now, or you may decide to wait.

Section 2.6

• Be sure to understand: The connection between Examples 2 and 3; the definition of continuity on page 157.

Note:
Read the formal definition of limit, but don't obsess over it.

Note 2:
There's a proof of the fact that the limit of sin(t)/t as t approaches 0 is 1 in Appendix H. (The book cites Appendix I, or at least my copy does). E-mail Subject Line: Math 101 Your Name 10/13

1. Let g(x)=(x2-9)/(x-3) as in Example 2, section 2.6
• Is g(x) defined at x=3? Why or why not?
• What is lim x->3 g(x)? Why?
2. Is n(x) in Example 8 (section 2.6) continuous at x=-3? Why or why not?

Due Monday 10/11 at 9am

Nothing! It's Fall Break!

Due Wednesday 10/13 at 9am

I hope you enjoy/enjoyed your break!
Section 2.6:

• Be sure to understand: The connection between Examples 2 and 3; the definition of continuity on page 157.

Note:
Read the formal definition of limit, but don't obsess over it. But beware--you used to have to learn and grasp this!

E-mail Subject Line: Math 101 Your Name 10/13

1. Let g(x)=(x2-9)/(x-3) as in Example 2, section 2.6
• Is g(x) defined at x=3? Why or why not?
• What is lim x->3 g(x)? Why?
2. Is n(x) in Example 8 (section 2.6) continuous at x=-3? Why or why not?

Reminders:

• The next problem set will be due this Friday; the only new material is 2.5, but there's some more problems from Section 2.3 and Section 2.4. Also, of course, if you didn't do the problems from Section 2.4 last week, as they weren't on the exam, this would be the time to do them!

Due Friday 10/15 at 9am

Section 2.7:

• To read: Skip Examples 4,5, and 7, and skip the squeeze principle. Read the rest.
• Be sure to understand: Examples 1 and 3; the section Finding Limits Graphically and Numerically
• Note: We're reading this section now to avoid having to read anything over break.

E-mail Subject Line: Math 101 Your Name 10/15

1. Find lim x->oo 1/x3 and explain.
2. Find limx-> 0 exp(sin(x)/x) and explain.

Here ends Chapter 2
Go to 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

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