Math 1572H Honors Calculus Spring Semester 2002

Assignment 6 - Due Thursday 3/7/2002

Hand in the starred (*) problems.

Read: Simmons, Sections 12.4, 13.1, 13.2, 13.2.

Exercises:

Sec. 12.4: 2, 4*, 8, 10*, 13, 17, 24a, 24b*, 24c, 24d. See also questions 24e*, 24f*, 24g below.
Page 426: 115*, 118
Sec. 13.2: 1b*, 1d, 1e, 1g, 1i, 9a*, 10a*, 14
Sec. 13.3: 2b, 2i, 2l*, 5b, 5e*, 5f, 5g*, 5h, 10a, 12

Question 23 on page 414 is quite important, and I think it is a pity that this piece of theory is put as an exercise. I will go over it in class. As well as the implications (a) and (b) stated in the question, there is also

There are also versions of these statements which apply to improper integrals which arise over a finite interval when the function tends to infinity.
You are supposed to use question 23 when doing 24, and the thing to note is that if an integral does converge, you are not asked to evaluate it, so don’t try to do that.

Here are some more integrals like those of question 24 on page 414: