Due date: Wednesday, 4/2/14
Last updated Mar 29 17:28 EDT 2014
You are required to do all of the problems below. You will not be required
to hand them all in. I’ve indicated below which ones you do have to hand in.
Don’t make the mistake of thinking that I’m collecting only the problems I
think are important. The “due date” above is the date that your written-up
problems should be handed in, but don’t wait to get started on the assignment.
You should always get started on problems as soon as we cover the relevant
material in class.
- A. Rosenlicht Chap. VI (pp. 132-135)/ 13, 23-26. Of these, hand in only
13 and 26. In your writeup of 26, you may assume the result of 25c.
In #25, Rosenlicht’s “hence that” is there for a reason: you are supposed
to figure out how the first part of the problem implies the limit-statements
in parts (a), (b) ,(c). Do not use l’Hôpital’s Rule, which is entirely unnecessary
for the computation of these limits, contrary to the impression you may have
received in Calculus 1. l’Hôpital’s Rule serves only to obscure the reason
that these limits are zero.You should also not use l’Hôpital’s Rule to help with 24cde. In any of these,
wherever you think you’d like to use l’Hôpital’s Rule, check whether the
definition of “derivative” would achieve the same purpose. (It should, unless
you’re doing something wildly wrong.) - A (continued). Rosenlicht Chap. VII (pp. 160-167)/ 3-5, 8-12. Of these,
hand in only 3, 9, and 12. In these exercises, remember that for a sequence of functions,
Rosenlicht’s “converges” is my “converges pointwise” (and similarly for “convergent”). - B. In the handout on improper integrals, do exercises through 1-16. These
problems are numerous but short. Of these, hand in only 14.