Math 1572H Honors Calculus Spring Semester 2002

Assignment 8 - Due Thursday 3/28/2001

Hand in the starred (*) problems.

Read: Simmons, Sections 13.5, 13.6, 13.7 and 13.8. In Section 13.6 we will not do any of the estimation on pages 458, 459 and 460. In particular, we will not do Euler's constant. In Section 13.7 we will not do the root test on the second half of page 463 and page 464. As usual the book goes on at some length, but the important thing is to grasp the basic ideas. For instance, the integral test says that if you have a sequence made up of the values of a positive decreasing function then the series converges precisely if the integral converges. That's it, and together with some practice to see the implications and get fluent, it is all you need to know.

Exercises:
Sec. 13.5: 1, 1e*, 1f*, 1h, 2, 3*, 4*, 6, 7, 9*, 11, 15, 18, 27*
Sec. 13.6: 1, 4*, 7, 8*
Sec. 13.7: 2*, 4*, 6, 8, 9, 10*
Sec. 13.8: 4, 6, 8, 18*, 20*, 23*, 24*, 25, 26

This might look like a lot of questions, but some of them are quite quick (or should be!). I am mindful of the suggestion to make the starred questions odd numbers, and I am not succeeding at this. Some of them are odd numbers, but also I am listing questions which appear to me to be interesting. I have listed many questions from section 13.5: in fact all of the questions at the end of section 13.5 are good practice. There are not so many questions at the end of sections 13.6 and 13.7, but there are more on these sections on pages 474 and 475.

Have a good break!