Math 327 A&B Spring 2014
Homework 6
Due in class on Friday, May 23
1. Determine whether the statement is true or false. Justify your answer.
(a) If
ak and
bk both converge, then
(ak bk ) must converge.
(b) If
ak converges absolutely and cfw_bk is bounded
Math 327 A&B Spring 2014
Additional Problems for Homework 3
Due in class on Friday, April 25
A1. (The Power Property for Limits) Suppose cfw_an converges to a and m N. Use
induction on m and the Product Property to prove that cfw_am converges to cfw_am
Math 327 A&B Spring 2014
Homework 4
Due in class on Friday, May 9
1. Determine whether each of the following series converges or diverges. If the series
converges, give its sum. Give complete and careful proofs of your answers.
(a)
k=1
(b)
k=1
3
4
k
3k 2
Math 327 A&B Spring 2014
Homework 7
Due in class on Friday, May 30
1. Dene f : R R by
f (x) =
3
x + 1 if x 4
2
if x > 3 .
4
Use the - denition of continuity to show that f is continuous at every x0 R
except x0 = 3 . (Note: This requires you to show that,
Math 327 A&B Spring 2014
Homework 8
This assignment will not be collected but you should do these problems to prepare for
the nal exam.
1. Dene f : R R by
f (x) =
3x 6 if x = 0
1
if x = 0.
Determine lim f (x) and use the - denition of a limit to prove tha
Math 327 A&B Spring 2014
Homework 5
Due in class on Friday, May 16
1. Determine whether each statement is true or false. Justify your answer.
(a) If
1
must diverge.
1 + ak
ak converges, then
(b) If ak 0 for all k N and
a2 converges, then
k
(c) If
ak conve