Fall 2001, Math 101

October 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 Monday 10/1 at 8am

Section 2.3 : The Geometry of Derivatives (again)

• Be sure to understand: Everything, much better than you did the first time around.

Reminder:

• Bring questions on PS 4 to class Monday.
• Problem Sets 4 and 4.5 (redoing the exam) are due Tuesday.
• If you were the primary author on the last group assignment, then you should not be the primary author this time around!

Due Wednesday 10/3 at 8am

Project 1
Guide to Writing Mathematics

• Be sure to understand: What your client is asking you to do! Also, the distinctions between writing up a problem set and a mathematics paper.

Reminders:

• Begin PS 5 (individual) Tuesday or Wednesday, and work on it throughout the week.
• Take advantage of a lighter-than-usual problem set by putting plenty of work into the the project.
• These projects are important, and I give you 1 1/2 weeks to work on them for a reason. The writing of the project is at least as important as the mathematics.

Due Friday 10/5 at 8am

Section 2.4: The Geometry of Higher Order Derivatives

• Be sure to understand: The second derivative test.

E-mail Subject Line: Math 101 Your Name 10/5

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?

Reminder:

• Plan on being done with the math and calculations for the project by Thursday 10/11 (Friday at the latest). With Fall Break coming up, this will require organization!
• You do have a reading assignment due the Wednesday you come back from break; make sure you get it done.

Monday 10/8: Enjoy your Fall Break!

Due Wednesday 10/10 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 10/10

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:

• Continue working on PS 5.
• Plan on being finished with the mathematics for the project by Thursday afternoon. Then get to work on writing up the results. Your first draft (which should not be especially rough) is due Monday 10/15 by 3:00 pm. The final draft will be due Friday 10/19 by 2:00pm.

Due Friday 10/12 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 10/12

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:

• When writing your draft of the project, remember to use the checklist and the writing guidelines!

Due Monday 10/15 at 8am

Section 2.6: Limits and Continuity
Section 2.7 : Limits Involving Infinity: New Limits from Old

• To read: All of Section 2.6. In Section 2.7, skip Examples 4,5, and 7; read the rest.
• Be sure to understand: In Section 2.6, the connection between Examples 2 and 3; the definition of continuity on page 157.

In Section 2.7, Examples 1 and 3; Theorems 1 through 4; the section Finding Limits Graphically and Numerically

Note 1:
Read the formal definition of limit, but don't obsess over it.
Note 2:
The proof 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 10/15

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

Reminder:

• 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. PS 5 is due, of course, Tuesday at the beginning of lab.
• Your draft of your project is due by Monday at 3:00pm.

Due Wednesday 10/17 at 8am

• To read: No new reading today. If you're feeling shaky on Sections 2.6 and/or 2.7, re-read them
• Be sure to understand: The intricacies of limits

Reminder:

• Begin working on PS 6 (group) Tuesday or Wednesday, and, as always, work on it throughout the week..
• As soon as I return your drafts, start working on your re-write. Remember not to only respond to my specific comments, but to use your own judgment while refining it -- really make it flow.

Due Friday 10/19 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 (the 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 10/19

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:

• Project 1 is due Friday by 3:00pm.

Due Monday 10/22 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 10/22

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:

• Bring questions on PS 6 to class Monday.
• I'm sure it doesn't need reminding, but PS 6 is due Tuesday at the beginning of lab.
• As always, if you were primary author on the last group assignment, then you shouldn't be primary author on this one! Be sure to get a cover sheet for your homework.
• If you feel you need extra assistance on the homework, or simply can not make my office hours, remember to take advantage of Meghan's help session, Monday nights at 8pm. If you're interested, e-mail her at mtracews before 5pm Monday.

Due Wednesday 10/24 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! Remember we've already seen that the limit of sin(t)/t as t approaches 0 in Section 2.6.
• Be sure to understand: Examples 1 and 2

E-mail Subject Line: Math 101 Your Name 10/24

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:

• Exam 2 will be Tuesday 3/27 during lab.
• Look at PS 7 (individual). This new material will be on the exam, so get an early start.

Due Friday 10/26 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 10/26

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:

• Try to get the problem set done by Friday afternoon or Saturday, so that you can focus on studying for the exam.

Due Monday 10/29 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:

• Problem Set 7 will be covered on the exam, so (as I've been nagging you) have it really truly done before class on Monday.
• Have worked out all the sample problems I gave you, and begin re-doing as many homework problems as possible.
• Bring questions on old material to class Monday.
• Before the exam Tuesday, write a "cheat sheet" if you want to. Same rules as before.
• If you feel you need extra assistance on the homework, or simply can not make my office hours, remember to take advantage of Meghan's help session, Monday nights at 8pm. If you're interested, e-mail her at mtracews before 5pm Monday.

Due Wednesday 10/31 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 10/31

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:

• Begin working onPS 8 (group) Tuesday or Wednesday, and work on it throughout the week. Re-doing Exam 2 is PS 8.5 (individual and optional).
• The differentiation exam is coming up on Monday. It doesn't take the same level of studying as the regular exams do, but do practice, practice, practice!

Here ends the reading for October
Go to the reading assignments for November!

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

Back to: Calculus 1 | My Homepage | Math and CS