Math H161 Brown 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  tk  in each subinterval to be the number which yields the maximum value of the function in that subinterval.  This function  f(x) = x3  increases as you go to the right, so that you will get an upper sum by letting  tk  be the right endpoint of each subinterval:  tk = xk. You would get lower sums for this function by letting each  tk = xk 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.)