e
Homework 5
Directions:
Determine the answers to the questions below. Then open the EMCF eHomework05
on CourseWare (
http://www.casa.uh.edu
) and submit your answers no later than Friday,
February 19
th
at 11:59pm.
1.
Every Cauchy sequence is bounded.
a.
True
b.
False
2.
Every monotone sequence is convergent.
a.
True
b.
False
3.
Every convergent sequence is a Cauchy sequence.
a.
True
b.
False
4.
According
to the lecture on 02/15, the Cauchy sequences are the ones that should
converge.
a.
True
b.
False
5.
According to the lecture on 02/15, the completeness axiom allows us to speak a number
into existence.
a.
True
b.
False
6.
Suppose
(
n
a
is a sequence.
If
(
n
na
converges then
(
0
n
a
→
.
a.
True
b.
False
7.
Suppose
(
n
a
is a sequence such that
0
n
a
for all
n
.
If
n
a
n
converges then
(
n
a
→ ∞
.
a.
True
b.
False
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 Spring '08
 Staff
 Mathematical analysis, Limit of a sequence, Cauchy sequence

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