- What is the 47th derivative of f(x)=exp(x)?

*exp(x) is Maple notation for the function e*^{x}. - Do exponential functions model population growth well? Explain.
- Draft of Project 1 is due by 2pm.
- Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
- Bring questions on PS 5.
- Just a mid-semester reminder, in case you've lost track: The point of these reading assignments is to give you credit for work you're doing anyway -- reading and beginning to learn the material. As I mentioned at the beginning of the semester, I do
**not**expect you to have completed learning the section by the time you answer these questions! Sometimes you'll be able to answer them correctly, and sometimes you won't -- either way is fine, as long as you make an effort. - Begin PS 6.
- What is limit( (cos(h)-1)/h, h=0)?
- What is limit( sin(h)/h, h=0)?
- Why do we care about the limits in the first two questions?
- Put plenty of time and thought into re-writing your projects. Feel free to bring your original rough drafts, or newer drafts, by for a consultation.
- f(x)=x^2*sin(x). f ' (x)=2*x*cos(x).
- g(x)=sin(x)/(x^2+1). g ' (x) = cos(x)/(2*x).
- Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
- Bring questions on PS 6.
- f(x)=sin(x^2). f ' (x) = cos(x^2)+sin(2*x)
- g(x)=exp(3*x). g ' (x)=exp(3*x).
- h(x)=(sin(x))^3. h ' (x)= 3*(cos(x))^2.
- Begin PS 7.
- The final draft of Project 1 is due by 4pm Friday.
- Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
- Bring questions on PS 7 to class.
- The Differentiation Exam will be given in lab Thursday.
- At which x-values can a continuous function f(x) achieve its maximum or minimum value on a closed interval [a,b]?
- What is the difference between an objective function and a constraint equation?
- Begin PS 8.
- Why would you want to find the Taylor polynomial of a function?
- In your own words, briefly explain the idea of building the Taylor polynomial for a function f(x).
- Bring questions on PS 8.

Spring 2004, Math 101

**March 2004**

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

(Last modified:
Wednesday, March 24, 2004,
4:47 AM )

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 Monday 3/1 at 10am**

**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.

**E-mail Subject Line:** Math 101 *Name* 3/1

**Reading questions:**

**Reminders:**

__ Due Wednesday 3/3 at 10am__

**Section 2.6 Derivatives of Exponential and Logarithmic Functions**

**To read:** Re-read this section, focusing on the derivatives of *e ^{x}* and

**No Reading Questions Today**

**Reminders:**

__ Due Friday 3/5 at 10am__

**Section 2.6 Derivatives of Exponential and Logarithmic Functions**

**To read:** Re-read this section *again*, focusing *this* time on the section on modelling growth.

**No Reading Questions Today**

**Reminder:**

__ Due Monday 3/8 at 10am__

**Section 2.7 Derivatives of Trigonometric Functions: Modeling Oscillation**

**To read:** All. Be sure to understand the section "Differentiating the sine: an analytic proof".

**E-mail Subject Line:** Math 101 *Name* 3/8

**Reading questions:**

**Reminder:**

__ Due Wednesday 3/10 at 10am__

**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 101 *Name* 3/10

**Reading questions:**

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

**Reminder:**

__ Due Friday 3/12 at 10am__

**Section 3.2 Composition and the Chain Rule**

**To read:**
Through Example 12. We'll consider evidence for why the Chain Rule is true during class.

**E-mail Subject Line:** Math 101 *Name* 3/12

**Reading questions:**

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

**Reminders:**

__ Monday 3/15- Friday 3/19__

**Spring Break!**

**Obviously, No Reading Questions These Days!**

__ Due Monday 3/22 at 10am__

**Reviewing Differentiation**

**To read:**
Review Chapter 2, and make sure it all makes sense now.

**No Reading Questions Today**

__ Due Wednesday 3/24 at 10am__

**Reviewing Differentiation**

**To read:**
Review Chapter 2 again, and this time, try to get a big picture for how it all fits together.
**No Reading Questions Today**

**Reminder:**

__ Due Friday 3/26 at 10am__

** Section 4.3 Optimization**

**To read: ** All. Read Examples 2, 3, and 4 carefully.

**E-mail Subject Line:** Math 101 *Name* 3/26

**Reading questions:**

__ Due Monday 3/29 at 10am__

** Section 4.3 Optimization**

**To read: ** Re-read the section carefully. Really work through the examples with pencil and paper and make sense of them.

**No Reading Questions for Today**

__ Due Wednesday 3/31 at 10am__

**Section 4.7 Building Polynomials to order: Taylor Polynomials**

**To read:**
All. Be sure to understand Examples 5 and 8.

**E-mail Subject Line:** Math 101 *Name* 3/31

**Reading questions:**

**Reminder:**

Go to the reading assignments for April!

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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