Reading Assignments for Calculus 1 with Econ Applications
Spring 2008, Math 102

January and February 2008

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

I'll use Maple syntax for some of the mathematical notation on this page. (Paying attention to how I type various expressions is a good way to absorb Maple notation). I will not use it when I think it will make the questions too difficult to read.
All section and page numbers refer to sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Volume 1, 2nd Edition, by Ostebee and Zorn.

Due Friday 1/25 at 9am

Section 1.1: Functions, Calculus Style
Section 1.2: Graphs

To read: The section How to Use This Book: Notes for Students beginning on page xvii. All of Sections 1.1 and 1.2.

E-mail Subject Line: Math 102 Name 1/25

Let f(x)=x^2.

1. How is the graph of y=f(x)+3=x^2+3 related to the graph of y=f(x)? Why?
2. How is the graph of y=f(x+3)=(x+3)^2 related to the graph of y=f(x)? Why?
3. Which of f(x), f(x)+2, f(x+2) are even? odd?

Reminders:

• In these assignments, you should always briefly explain how you arrived at your answers.
• Begin PS 1, listed at the bottom of this course's web page. The problem sets due each Tuesday reflect an entire week's worth of work, and you should be working on them throughout the week.

Due Monday 1/28 at 9am

Problem Set Guidelines
Section 1.3 A Field Guide to Elementary Functions

To read: All of Section 1.3. Be sure to understand the definition of the logarithm function base b and the definitions of sin(x) and cos(x) in terms of the unit circle. If you are not particularly comfortable with exponential functions or trig functions, work through the appropriate appendices.

E-mail Subject Line: Math 102 Name 1/28

1. How are the functions f(x)=3^x and g(x)=log[3](x) related?
log[3](x) is Maple notation for log3(x).
2. What are some of the properties of sin(x)?

Reminders:

• Come to lab Tuesday at 1pm!
• PS 1, which is an individual assignment, is due Tuesday at the beginning of lab. Read and follow the hw guidelines referred to above.
• If you're having difficulties with the problem set, or if you'd just like to make sure you're on the right track, come to my office hours and/or visit the Kollett Center during the Calc tutoring hours.
• If you have any remaining questions on the problem set after coming to my office hours and visiting the Kollett Center, bring them to class Monday.
• Make sure you've read all the stuff I handed out in class and all the material on the course web page.

Due Wednesday 1/30 at 9am

Section 1.3 A Field Guide to Elementary Functions

To read: Re-read Section 1.3. If you feel shaky with exponential functions, log functions, or trig functions, read the appropriate appendices in the back of the book. (I have copies!) We won't be using these ideas right away, so don't panic, but do take the time to learn these functions -- we'll be using them all term.

Reminder:

• Begin PS 2. This is a group assignment. Groups ideally consist of two people. In a pinch, three will do; more than that is not okay. Find a partner now, but most people find they learn the most if they begin the problems on their own, and then get together to discuss them. Do not split the problems up between you (see the discussion of the Honor Code in the course policies.

Due Friday 2/1 at 9am

Section 1.4 Amount Functions and Rate Functions: The Idea of the Derivative

E-mail Subject Line: Math 102 Name 2/1

Look at the graphs of P(t) and V(t) in Figure 1 on page 37.

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.

Reminder:

• The point of reading assignments is to give you credit for reading and for beginning the learning process. I do not expect you to have mastered the section by the time you answer these questions! Use this as an opportunity to identity the material you find particularly mysterious before class.
• Office Hours and/or tutoring hours are an important part of Calculus; do not hesitate to take advantage of them.

Due Monday 2/4 at 9am

Section 1.5 Estimating the Derivative

E-mail Subject Line: Math 102 Name 2/4

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

Reminders:

• Your group will turn in one joint version of PS 2; the recopying should all be done by one person, the "primary author". Put a star next to the name of the "primary author".
• If, after coming to office hours, you still have questions on PS 2, bring them to class on Wednesday.
• Be sure that each member of your group has a photocopy of the problem set you turn in, both for studying purposes and for your records.
• I suggest that you switch partners with every group problem set. You should be the primary author roughly every other group problem set.

Due Wednesday 2/6 at 9am

Section 1.6 The Geometry of Derivatives

To read: All. Be sure to understand the definition of a stationary point and the difference between local and global maxima and minima.

E-mail Subject Line: Math 102 Name 2/6

Look at the graph of f ' in Example 2.

1. Where does f have stationary points? Why?
2. Where is f increasing? Why?
3. Where is f concave up? Why?

Due Friday 2/8 at 9am

Section 1.7 The Geometry of Higher Order Derivatives

To read: All. Think about why the Second Derivative Test makes sense.

E-mail Subject Line: Math 102 Name 2/8

Use the graphs of f, f ', f '' in Figure 3 on page 67.

1. By looking at the graph of f '', how can you tell where f is concave up and concave down?
2. By looking at the graph of f ', how can you tell where f is concave up and concave down?

Due Monday 2/11 at 9am

Section 2.1 Defining the Derivative

To read: All. We'll talk about the formal definition of the derivative in detail during class.

E-mail Subject Line: Math 102 Name 2/11

1. Let f(x)=x^3. 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)=x^3. What is the average rate of change of f from x=-2 to x=4?

Reminders:

• Bring questions on PS 3 to class.

Due Wednesday 2/13 at 9am

Work on Project 1

Reminder:

• Exam 1 will be Tuesday 2/19. Because of it, PS 4 will not be collected, but should be completely done by the beginning of class on Monday.

Due Friday 2/15 at 9am

Section 2.2 Derivatives of Power Functions and Polynomials

To read: Through Theorem 4 on page 97. Be sure to understand Examples 1 and 2.

E-mail Subject Line: Math 102 Name 2/15

1. What is the derivative of f(x)=x^3?
2. Let f(x)=x^(1/3) (i.e. the cube root of x). Use the graph of y=f(x) to explain why f'(x) does not exist at x=0.
Reminder:
• As you study for Exam 1, remember to visit the Kollett Center, as well as my office hours!

Due Monday 2/18 at 9am

Bring Questions for Exam 1

Reminders:

• As you prepare for the exam, be sure to take advantage of all the Kollett Center has to offer, as well as my office hours!
• Get questions on PS 4 out of the way before class! This problem set should be finished before class, so you can be focusing on reviewing the semester to date.
• For the exam, you may have a "cheat sheet", consisting of handwritten notes on one side of an 8 1/2 x 11 (or smaller) piece of paper.
• You may begin taking the exam at 12:30pm Tuesday.

Due Wednesday 2/20 at 9am

Section 2.3 Limits

To read: All. Be sure to understand Example 4 and the definitions of left-hand and right-hand limits.

E-mail Subject Line: Math 102 Name 2/20

1. Let g(x)=(x^2-9)/(x-3), as in Example 2.
1. Is g(x) defined at x=3? Why or why not?
2. What is limit(g(x),x=3)? Why?
2. Is f(x)=|x| continuous at x=0? Why or why not?

Due Friday 2/22 at 9am

Section 2.4 Using Derivative and Antiderivative Formulas

To read: All. Be sure to understand the definition of an antiderivative and Theorems 8, 9, and 10.

E-mail Subject Line: Math 102 Name 2/22

1. Explain in your own words what an antiderivative of a function g(x) is.
2. How many antiderivatives does f(x)=3x^2 have? Why?

Reminder:

• Read the guidelines and the checklist before beginning to write your letter. It will not be easy to write, so leave plenty of time.

Due Monday 2/25 at 9am

Section 2.6 Derivatives of Exponential and Logarithmic Functions; Modelling Growth

To read: All. Be sure to understand Theorem 12 and the section "Proof by picture" that follows. You'll note we're skipping Section 2.5, on differential equations. If we have time at the end of the semester, we'll go back to that important side issue for as long as we can. Meanwhile, both this section and the next will mention differential equations (abbreviated DEs). When the book is discussing DEs, don't focus on the details of working through the examples, but do try to get a sense for what sort of problems these functions are useful for.

E-mail Subject Line: Math 102 Name 2/25

1. What is the 47th derivative of f(x)=exp(x)?
exp(x) is Maple notation for the function ex.
2. What sort of growth do compound-interest bearing accounts exhibit (more or less)?

Reminders:

• Bring questions on PS 5 to class
• Just a mid-semester reminder: The point of these reading assignments is to give you credit for work you're doing anyway (or should be doing) -- reading and beginning to learn the material. Remember, I do not expect you to have completely mastered the section by the time you answer these questions!

Due Wednesday 2/27 at 9am

Section 2.7 Derivatives of Trigonometric Functions: Modeling Oscillation

To read: All. Give a real try at understanding the section "Differentiating the sine: an analytic proof".

E-mail Subject Line: Math 102 Name 2/27

1. What is limit( (cos(h)-1)/h, h=0)?
2. What is limit( sin(h)/h, h=0)?
3. Why do we care about the limits in the first two questions?
4. Differentiate sin(2x).
Reminder:
• Put plenty of time and thought into writing the final drafts of the projects.
• PS 6 is another group assignment. I urge you to switch partners. If you were not the primary author last time, you should be this time. As always, do not split up the problems between you.

Due Friday 2/29 at 9am

Section 3.1 Algebraic Combinations: The Product and Quotient Rules

To read: All. Be sure to understand Examples 3, 4, and 5.

E-mail Subject Line: Math 102 Name 2/29

Explain what is wrong with the following calculations and fix them.

1. f(x)=x^2*sin(x). f ' (x)=2*x*cos(x).
2. g(x)=sin(x)/(x^2+1). g ' (x) = cos(x)/(2*x).

Reminder:

• The project is due by 3pm Friday.

Here ends the reading for January and 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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