- What are the
**hypotheses**of the Mean Value Theorem? - What is the
**conclusion**of the Mean Value Theorem? - Explain the MVT using "car talk" -- that is, using velocity.
- The deadline for receiving 90% on the Differentiation Exam is Friday at 3pm.
- What does the integral of a function f from x=a to x=b measure?
- Is the integral of f(x)=5x from x=-1 to x=3 positive or negative?
- The deadline for receiving 90% on the Differentiation Exam is Friday at 3pm.
- The mathematical calculations for the project should be done by Friday afternoon.
- Let f be any function. What does the area function A
_{f}(x) measure? - Let f(t)=t and let a=0. What is A
_{f}(1)? - Bring remaining questions on PS 10 to class.
- If you haven't already, finish the calculations for the project, and get a good start on writing the letter. If you want to feedback on a rough draft, bring one by earlier enough that I have time.
- Find the area between the x-axis and the graph of f(x)=x^3+4 from x=0 to x=3.
- Does every continuous function have an antiderivative? Why or why not?
- If f(x)=3*x-5 and a=2, where is A
_{f}increasing? Decreasing? Why? - How would your answer change if a=0?
- Project 2 is due by 3:00pm Friday.
- Explain the fundamental difference between a definite integral and an indefinite integral. Please go deeper than saying one has limits of integration and one doesn't. The first is a real number --
*why?*What does it represent? Then think similarly about an indefinite integral? Is it a real number? If not what is it? Why? What does it represent? - Substitution attempts to undo one of the techniques of differentiation. Which one is it?
- What are the three steps in the process of substitution?
- Bring questions on PS 11.
- The deadline to receive 75% on the Diff Exam is Friday at 3pm.
- Exam 3 is on Tuesday 4/22. As usual, get an early start on PS 12.
- Explain, in your own words, the idea of using Riemann Sums to approximate integrals.
- If f(x) is decreasing on [a,b], will L
_{n}underestimate or overestimate the integral of f from a to b? How about R_{n}? - The deadline to receive 75% on the differentiation exam is Friday at 3pm.
- Visit my office hours and visit the Kollett Center while clearing up questions before the exam!
- Get questions on PS 12 out of the way
**before**class. PS 12 should be done before class so that you can focus on reviewing. - As usual, 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 for the exam. - As before, you may begin taking the exam at 12:30pm Tuesday.
- Show that y(x)=x^(1/3) is a solution to the differential equation y'(x)=1/(3*y^2).
- Solve the initial value problem y'(x)=5/x^2+4, y(1)=12.
- TBA
- The deadline to receive 50% on the Diff Exam is Friday at 3pm.
- The deadline to receive 50% on the Diff Exam is Friday at 3pm.
- The final will be Saturday, May 10, from 2pm-5pm.

Spring 2008, Math 102

**April and May 2008**

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

(Last modified:
Monday, January 21, 2008,
3:42 PM )

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 4/2 at 9am__

**Section 4.9 Why Differentiability: The Mean Value Theorem**

**To read:** All. Be sure to understand the statement of the Mean Value Theorem and the section "What the MVT says."

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

**Reading questions:**

**Reminder:**

__ Due Friday 4/4 at 9am__

**Section 5.1 Areas and Integrals**

**To read:** All. Be sure to understand the definition of the integral, Example 2, and the section "Properties of the Integral" beginning on page 306.

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

**Reading questions:**

__ Due Monday 4/7 at 9am__

**Section 5.2 The Area Function**

**To read:** All. Make sure you understand the definition of the area function and Examples 2, 3, and 4.

**E-mail Subject Line:** Math 102 *Name* 4/7

**Reading questions:**

**Reminder:**

__ Due Wednesday 4/9 at 9am__

**Section 5.3 The Fundamental Theorem of Calculus**

**To read:** All, but you can skip the proof of the FTC if you'd like: we'll look at a different approach in class.

**E-mail Subject Line:** Math 102 *Name* 4/9

**Reading questions:**

__ Due Friday 4/11 at 9am__

**Section 5.3 The Fundamental Theorem of Calculus**

**To read:** Re-read this section.

**No Reading Questions Today!**

**Reminder:**

__ Due Monday 4/14 at 9am__

**Section 5.4 Finding Antiderivatives: The Method of Substitution**

**To read:**
All. Be sure to understand Examples 8, 9, and 10.

**E-mail Subject Line:** Math 102 *Name* 4/14

**Reading questions:**

**Reminder:**

__ Due Wednesday 4/16 at 9am__

**Section 5.4 Finding Antiderivatives: The Method of Substitution**

**To read:**
Re-read the section carefully.

**No Reading Questions Today**

**Reminders:**

__ Due Friday 4/18 at 9am__

**Section 5.6 Approximating Sums: The Integral as a Limit**

**To read:**
All. Be sure to understand the definitionof a Riemann Sum and Example 3.

**E-mail Subject Line:** Math 102 *Name* 4/18

**Reading questions:**

__ Due Monday 4/21 at 9am__

**Bring Questions for Exam 3**

**No Reading Questions Today**

**Reminders:**

__ Due Wednesday 4/23 at 9am__

**Section 5.6 Approximating Sums: The Integral as a Limit**

**To read:**
Re-read and understand this section.

**No Reading Questions Today**

** Due Friday 4/25 at 9am**

**Section 2.5 Differential Equations; Modelling Motion**

**To read:**
All. Be sure to understand the difference between solutions to algebraic equations and to differential equations; Examples 1, 2, 3, and 6.

**E-mail Subject Line:** Math 102 *Name* 4/25

**Reading questions:**

** Due Monday 4/28 at 9am**

**Section 2.5 Differential Equations; Modelling Motion**

**To read:**
Re-read this section.

**No Reading Questions Today!**

** Due Wednesday 4/30 at 9am**

**TBA**

**To read:**
TBA

**Reading Questions:**

** Due Friday 5/2 at 9am**

**The Big Picture**

**To read:**
Review Section 5.6 and 2.5; begin reviewing the entire semester.

**No Reading Questions Today!**

**Reminders:**

**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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