- 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.
- Bring questions on PS 5.
- Office hours and other outside help are just part of Calculus -- make the time to come see me and/or see the tutors in the CLC.
- 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?
- Differentiate sin(2x).
- Is y=sin(2x) a solution to the DE y''=4y?
- 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).
- Please make use of my office hours for not only issues with understanding material or questions on homework, but also for suggestions on improving your project.
- 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.
- Please continue taking advantage of office hours and the CLC!
- 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.
- If you didn't succeed at the differentiation exam the first time around, come by my office as soon as possible to give it another shot. Don't put it off until you feel confident -- part of the point of these exams is to give you however much experience you need to master differentiation!
- If you haven't yet succeeded at the differentiation exam, keep on coming trying.
- Bring remaining questions on PS 8 to class Wednesday.
- 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).
- Keep on taking advantage of the CLC and of my office hours!
- Bring remaining questions on PS 8 to class Wednesday.

Spring 2005, Math 101

**March 2005**

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

(Last modified:
Sunday, March 20, 2005,
10:43 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 Wednesday 3/2 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.

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

**Reading questions:**

**Reminders:**

__ Due Friday 3/4 at 9am__

**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**

**Reminder:**

__ Due Monday 3/7 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 101 *Name* 3/7

**Reading questions:**

__ Due Wednesday 3/9 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 101 *Name* 3/9

**Reading questions:**

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

**Reminder:**

__ Due Friday 3/11 at 9am__

**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* 3/11

**Reading questions:**

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

**Reminders:**

__ Monday 3/14- Friday 3/18__

**Spring Break!**

__ Due Monday 3/21 at 9am__

**More On Differentiation**

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

**No Reading Questions Today**

__ Due Wednesday 3/23 at 9am__

**The Big Picture On Differentiation**

**To read:**
Practice as many differentiation problems as you can. Make some up, even!

**No Reading Questions Today**

**Reminder:**

__ Due Friday 3/25 at 9am__

** Section 4.3 Optimization**

**To read: ** All. Don't worry about the fact that we skipped the section on implicit differentiation. We can do any and all optimization problems without it. (If we have time at the end of the semester, we'll go back to the section on implicit differentiation.) Read Examples 2, 3, and 6 carefully. In example 4, the text says "we *could* use the constraint *x+y=10* to solve for *y* and then rewrite *P* as a function of *x* alone." -- try to figure out what they're talking about, as that's the way we'll approach such problems.

**E-mail Subject Line:** Math 101 *Name* 3/25

**Reading questions:**

__ Due Monday 3/28 at 9am__

** 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**

**Reminder:**

** Due Wednesday 3/30 at 9am**

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

**To read:**
All. (Yes, we skipped sections again. Chapter 4 is selected applications -- I'm picking and choosing among them. If we have time at the end of the semester, we'll go back to Sections 4.5 and 4.6.)Be sure to understand Examples 5 and 8.

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

**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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