Math H161 Ð Brown Ð Au04

Homework 2, due Wednesday, October 6, 2003

This homework has a lot of short problems, except for Problem 3, which is somewhat longer. Don't leave them until the night before they are due!

Caution: In this homework set, whenever you are asked to find an area, be sure to sketch the graph before doing the calculations for the area.

1. Textbook, page 177: #2, 4, 8, 16, 18, 26, 32, 37, 46, 50, 58, 63a, b, c, d

2. Textbook, page 212-213: #6, 8, 10, 16, 24, 30, 42

3. Textbook:
page 206: #1. Hint: you get an "upper sum" when
you choose the number t_{k} in each subinterval to be the number which yields the
maximum value of the function in that subinterval. This function
f(x) = x^{3} increases as you go to the right, so
that you will get an upper sum by letting
t_{k} be the right endpoint of each
subinterval: t_{k} = x_{k}.
You would get lower sums for this function by letting each t_{k}
= x_{k Ð 1}.)

Here is the "thinking" problem for this homework.

4. Textbook, page 217, #13. (Hint : Write down a definite integral which expresses the area of a semicircle of radius a with center at the origin, and set that integral equal to the value you already know from elementary geometry for the area of a semicircle.)