e
Homework 10
Homework Directions:
Determine the answers to the questions below. Then open the EMCF
eHomework10 on CourseWare (
http://www.casa.uh.edu
) and submit your answers no later than
Tuesday, April 13
th
at 11:59pm.
Note:
We will assume that
D
is a nonempty subset of
R
,
f
and
g
are functions from
D
to
R
,
and
c
is an accumulation point of
D
.
1.
( 29 ( 29
( 29 ( 29 ( 29
lim
lim
lim
x
c
x
c
x
c
f x
g x
f x
g x
→
→
→
+
=
+
.
a.
True
b.
False
2.
( 29 ( 29 ( 29 ( 29
lim
lim
lim
x
c
x
c
x
c
f x g x
f x
g x
→
→
→
=
.
a.
True
b.
False
3.
If
( 29 ( 29
( 29
lim
x
c
f x
g x
→
+
and
( 29
lim
x
c
g x
→
both exist, then
( 29
lim
x
c
f x
→
exists.
a.
True
b.
False
4.
If
f
(
x
) > 0
for all
x
, and
( 29 ( 29
lim
x
c
f x g x
→
exists, then
( 29
lim
x
c
g x
→
exists.
a.
True
b.
False
5.
If
D
is compact, then
( 29 ( 29
lim
x
c
f x
f c
→
=
.
a.
True
b.
False
6.
If
D
is compact, then
f
has a maximum value.
a.
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 Spring '08
 Staff
 Topology, Metric space, Compact space, Closed set

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