Fall 2001, Math 101

December 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 Monday 12/3 at 8am

The Area Function

• Be sure to understand: Everything

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

Suppose that f (x) = 4x+2. Let Af(x) be the area function from 0 to x of f.
1. What is Af(1)?

2. What is Af(x), if x>0?

Due Wednesday 12/5 at 8am

Section 5.3: The Fundamental Theorem of Calculus

• To read: All, although you may skim the proof of the FTC beginning on page 373-we'll prove it a different way in class.
• Be sure to understand: The statement of both the first and second forms of the FTC; Example 3

E-mail Subject Line: Math 101 Your Name 12/5

1. Find the area between the x-axis and the graph of f(x)=x3+4 from x=0 to x=3.
2. Does every continuous function have an antiderivative? Why or why not?
3. What is the difference between a definite integral and an indefinite integral?

Reminder:

• Begin working on PS 13 Tuesday or Wednesday, and work on it throughout the week.
• The final exam is Saturday 12/15 at 2pm. I don't know the location, but you can find it out by looking around for the postings on the walls.
• The final will be cumulative, of course. Begin reviewing now (or sooner) and get help on anything you never understood, or used to understand and don't anymore, or mostly understand . Please ask me about anything you've never understood, whether it's basic or deep, old or new.

Due Friday 12/7 at 8am

Section 5.4 : Approximating Sums: The Integral as a Limit

• To read: Through page 381
• Be sure to understand: The figures on page 381

E-mail Subject Line: Math 101 Your Name 12/7

Let f(x)=x2 and let I represent the integral of f from x=0 to x=3.
1. Estimate I by finding L3, the left sum with 3 equal subintervals.
2. Estimate I by finding R3, the right sum with 3 equal subintervals.

Due Monday 12/10 at 8am

Section 5.4: Approximating Sums

• Be sure to understand: The definition of a Riemann sum and the definition of the integral as a limit on page 383.

E-mail Subject Line: Math 101 Your Name 12/10

Let f(x)=x2 and let I represent the integral of f from x=0 to x=3.
1. Will Ln underestimate or overestimate I? Why?
2. Will Rn underestimate or overestimate I? Why?

Reminder:

• Again, the final is Saturday 12/10 at 2pm.
• You may have a "cheat sheet" on the final, but the same rules apply as before: it still must be just the front of a standard-sized sheet of paper, and the notes must be handwritten (by you) -- i.e. no shrinking your three previous ones onto one sheet!

Here ends the reading for the semester!

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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