Spring 2001, Math 101

March 2001

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

All section and page numbers refer to sections from Ostebee/Zorn, Vol 1.

Due Friday 3/2 at 8am

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. Take notes while you're reading (as you should always be doing). Try to work out the connection between one sentence and the next or one line of mathematics and the next, if it is not immediately obvious to you.
• Be sure to understand: Example 1; page 43: Average Speeds, Instantaneous Speeds, and Limits; the formal definition of the derivative.

E-mail Subject Line: Math 101 Your Name 3/2

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:

• Work on PS 5.
• Plan on being finished with the mathematics for the project by Monday afternoon, so that you can start writing it and bring me a rough draft to look at Tuesday or (at the absolute latest) Wednesday. You don't want to get a score in the 50s or 60s just because you didn't understand what I mean by "explain in language your audience can understand", for instance.

Due Monday 3/5 at 8am

Section 2.5 : Average and Instantaneous Rates: Defining the Derivative
Guide to Writing Mathematics

• To read: Re-read the Writing Guide and Section 2.5. I had you read Section 2.5 for Friday as well as for today so that you'd have several days to absorb the material. Really work through each sentence and each example.
• Be sure to understand: Example 1; page 43: Average Speeds, Instantaneous Speeds, and Limits; the formal definition of the derivative, just as before.

E-mail Subject Line: Math 101 Your Name 3/5

Let f(x) = x3 (as we did on Friday).
1. Find the slope of the secant line from x= 1 to x=3.
2. Find the slope of the secant line from x=1.9 to x=2.1.
3. Which of these do you think is closer to the slope of the tangent line at x=2?
4. What is the average rate of change of f for x between x=1 and x=3? What is the average rate of change of f for x between x=1.9 to x=2.1? Which of these do you think is closer to the rate f is changing when x=2?
5. What does the quotient [f(x)-f(a)]/[x-a] represent?

Reminders:

• Bring questions on PS 5 to class on Monday. As always, I just want to remind you of our help sessions and my office hours.
• I can not emphasize enough how important it is that you be done with the calculations for Buffy by Monday, so that you have the whole week to figure out how in the world to explain to her what you did in a way she can understand and follow.

Due Wednesday 3/7 at 8am

Section 2.6: Limits and Continuity

• To read: All of 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 3/7

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?

Reminder:

• Look at PS 6 (group). It's due right after break, so get an early start on it. Remember to switch recorders from last time.
• Bring a rough draft of your letter to Buffy to me for us to discuss together -- preferably by Wednesday.

Due Friday 3/9 at 8am

Section 2.7 : Limits Involving Infinity: New Limits from Old

• Be sure to understand: Examples 1 and 3; Theorems 1 through 4; the section Finding Limits Graphically and Numerically

E-mail Subject Line: Math 101 Your Name 3/9

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

Reminder:

• Project 1 is due Friday by 4:00pm.
• You do have a reading assignment due the Monday after break.

Monday 3/12 through Friday 3/16: Spring Break

Due Monday 3/19 at 8am

Section 3.1: Derivatives of Power Functions and Polynomials
Section 3.2: Using Derivatives and Antiderivative Formulas

• To read: All of Section 3.1 (he optional section is indeed optional.)
All of Section 3.2.
Also re-read Free Fall with Resistance and Example 4 in Section 2.1.
• Be sure to understand: In Section 3.1: Examples 1 and 2; Theorems 1, 2 , and 3; the definition of an antiderivative.
In Section 3.2: Examples 2 and 4

E-mail Subject Line: Math 101 Your Name 3/19

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:

• Bring questions on PS 6 to class Monday.
• Exam 2 will be Tuesday 3/27 during lab.

Due Wednesday 3/21 at 8am

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 3/21

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:

• Look at PS 7 (individual). This new material will be on the exam, so get an early start.

Due Friday 3/23 at 8am

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 3/23

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:

Due Monday 3/26 at 8am

Question and Answer for Exam 2

• To read: Re-read the text and your notes from since the last exam. (You may need to review some of the material that was covered on the last exam as well.)
• Be sure to understand: All of it!

Reminder:

• As with before the last exam: have done all the problems due Tuesday before Monday's class, as this new material will be on the exam.
• Have worked out all the sample problems I gave you, and begin re-doing as many homework problems as possible.
• Write down at least one question on the material to hand to me at the beginning of class Monday.
• Before the exam Tuesday, write a "cheat sheet" if you want to. Same rules as before.

Due Wednesday 3/28 at 8am

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 3/28

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

Reminders:

• Look at PS 8 (group). Re-doing Exam 2 is PS 8.5 (individual and optional).

Due Friday 3/30 at 8am

Section 3.6: New Derivatives from Old: The Chain Rule

• Be sure to understand: Theorem 11 and Example 3

E-mail Subject Line: Math 101 Your Name 3/30

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:

• The differentiation exam is coming up on Wednesday. Practice, practice, practice!

Here ends the reading for March
Go to the reading assignments for April!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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