Spring 2001, Math 101

February 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 2/2 at 8am

Section 1.2 : Graphs
Section 1.3: Machine Graphics
Section 1.4: What Is A Function?

• To read: Finish Section 1.2, read all of Section 1.3, and read Section 1.4 through the middle of page 41.
• Be sure to understand: Section 1.2: New Functions from Old
Section 1.3: Six views of the sine function, Examples 1 and 2
Section 1.4: Both definitions of a function, the five examples, and the definitions of domain and range.

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

1. Suppose f (x) is any function. How does the graph of f (x)+2 compare with the graph of f (x)? The graph of 2 f(x) compare to f (x)?
2. Calculate h (1/2), where h is the third of the five examples in Section 1.4.
3. Let g (t)= the world's human population t years C.E, as in the second of the five examples in Section 1.4. What are the domain and range of g (t)?
4. Find the domain and range of m (x)=x 2.

Reminders:

• Work on PS 1. If you have questions on some of those (whose material we have already covered), bring them to my office hours. If you can't make my office hours, please e-mail me about making an appointment, or just stop by and see if I'm free.

Due Monday 2/5 at 8am

Section 1.4: What Is A Function?
Section 1.5: A Field Guide To Elementary Functions
Appendix B: Lines and Linear Functions
Appendix C: Polynomial Algebra

• To read: Finish Section 1.4, and read through Other Algebraic Functions in Section 1.5. Read or skim Appendices B and C with whatever depth you need to.
• Be sure to understand: In Section 1.4, Periodic Functions, the symbolic view .
In Section 1.5, all of Algebraic Functions , Example 2, and the discussion of asymptotes in Example 3.
All of appendices B and C.

E-mail Subject Line: Math 101 Your Name 2/5

1. How can you recognize a periodic function from its graph?
2. In Example 3 on page 54, what are the domain and range of the rational function r (x) ? What is the relationship between the domain, the range, and the asymptotes?

Reminders:

• PS 1 (individual) is due Tuesday at 4:00pm.
• Bring questions on PS 1 to class on Monday. Bring any remaining questions to my office hours.
• If after class Monday, and office hours, you still have questions remaining, please e-mail the class assistant to tell her you'd like to attend the help session Monday evening.
• Remember to come to lab at 1:00pm Tuesday.

Due Wednesday 2/7 at 8am

Section 1.5 : A Field Guide to Elementary Functions
Appendix E: Algebra of Exponentials
Appendix F: Algebra of Logarithms

• To read: Exponential and Logarithm Functions, Exponential and Logarithm Functions as Inverses (i.e. middle of page 54 - middle of page 61). Read or skim the two appendices at whatever depth you need to, but especially logarithms are tricky for people, so don't be lazy! Make sure you really work at these!
• Be sure to understand: The appendices. The definitions of exponential and logarithmic functions, the relationship between all graphs of exponential functions, the relationship between all graphs of logarithmic functions, the common points of each, and the relationship between the graph of a function bx and logbx.

E-mail Subject Line: Math 101 Your Name 2/7

1. Is ey an exponential function? How about (Pi)x? ze?Why or why not?
2. If you were shown the graph of a monotonically increasing function, what would you look for to decide whether it could be an exponential function, or to eliminate that possibility?
3. What logarithm function corresponds to the exponential function 3x? How are the log function you found and 3x related?

Reminder:

• Look at PS 2 on the course web page. PS 2 is a group assignment, so find a congenial person to work with.

Due Friday 2/9 at 8am

Section 1.5: A Field Guide To Elementary Functions
Appendix G: Trigonometric Functions

• To read: Finish Section 1.5, and read or skim Appendix G.
• Be sure to understand: The sine and cosine functions defined as circular functions; every point on the unit circle corresponds to a value of both the sine and the cosine functions.

E-mail Subject Line: Math 101 Your Name 2/9

1. Can sin(x)=2 for some value of x? Why or why not? What are the domain and range of sin(x)?
2. Explain, in more detail than the book does, why sine and cosine are each 2 Pi periodic.
3. Evaluate sin2(38)+cos2(38) without a calculator. Explain (of course).

Reminder:

• As always come see me if you have any questions, or any vague sense that you're not getting as much as you want to. Don't wait -- if you end up being lost, it's hard to recover.

Due Monday 2/12 at 8am

Section 1.6 : New Functions From Old

• To read: Through Example 4
• Be sure to understand: The definition of the composition of two functions, the examples that shows that order matters.

E-mail Subject Line: Math 101 Your Name 2/12

1. Using f and g in Example 2, what is (g o f)(2)?
2. Let f(x)=x3 and g(x)=sin(x).
• What is (f o g)(x)?
• What is (g o f )(x)?

Reminder:

• PS 2 is due Tuesday. Your group should turn in one joint version. Photocopy it before turning it in (and again when you get it back from the grader), so that you each have a copy for studying purposes (and so you have a record of your scores). Remember to note on your joint problem set who the "recorder" was--the person who did the writing. (A star by that person's name will suffice). Next time, switch recorders.
• Bring questions on PS 2 to class on Monday. If after class you still have questions, come to my office hours. Remember, also, to take advantage of our Calc help hour Monday nights.

Due Wednesday 2/14 at 8am

Section 2.1: Amount Functions and Rate Functions: The Idea of A 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

E-mail Subject Line: Math 101 Your Name 2/14

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:

• Look at PS 3 (individual).
• Exam 1 will be given in lab Tuesday 2/20. Start studying! Spread it out over many days, and be sure to do the study guide I'm giving you as well as re-reading the text and your notes, and re-doing as many homework problems as you possibly can.

Due Friday 2/16 at 8am

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 2/16

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

Reminders:

• Exam 1 will cover the material from Friday's class, so get an early start on the problems and make sure you really understand the recent concepts.
• Once again, let me remind you to come to office hours!

Due Monday 2/19 at 8am

Questions and Answers for Exam 1

• To read: Re-read the text and your notes from the beginning of the semester up through Section 2.2.
• Be sure to understand: All of it!

Reminder:

• In addition to the exam, PS 3 is due Tuesday. The exam will cover PS 3, so be sure to put quality effort into it.
• Review over the week-end, of course. Have tried every one of the sample problems, and have begun re-doing old homework.
• Write down at least one question to hand to me at the beginning of class Monday.
• Before the exam Tuesday, write a "cheat sheet" if you want to. It must be only on one side of standard 8 1/2" x 11" paper, and it must be handwritten by you. You may put write anything on it you want to, but you must do the writing.
• Remember: Carol is available for help at 9:30 in A102 -- but you must e-mail her before 6pm at cmcgeoch to let her know you'd like to meet with her.

Due Wednesday 2/21 at 8am

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 2/21

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?

Reminders:

• Look at PS 4 (group). Be aware that re-doing the exam (on your own, except for help from me) will be an additional optional assignment (PS 4.5).

Due Friday 2/23 at 8am

Section 2.3 : The Geometry of Derivatives (again)

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

Due Monday 2/26 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 2/28

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:

• Problem Sets 4 and 4.5 are due Tuesday. Bring questions on Section 2.3 to class Monday. I will not be answering questions on the exam in class, but I would be delighted to help in office hours (as always). Also as always, remember to take advantage of our Calc Help Hour.
• The recorder for PS 4 should not be the same as the recorder for PS 2.
• Remember: Carol is available for help at 9:30 in A102 -- but you must e-mail her before 6pm at cmcgeoch to let her know you'd like to meet with her.

Due Wednesday 2/28 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:

• Look at PS 5 (individual).
• Take advantage of two lighter-than-usual problem sets in a row by putting plenty of early 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.

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

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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