le (chl528) – HW03 – Gilbert – (57195)
2
4.
both I and II
correct
Explanation:
003
(part 2 of 2) 10.0 points
(ii) Which of the following statements are
true for all
c
and all
L
?
I. lim
x
→
c
f
(
x
)=
L
=
⇒
lim
x
→
c

f
(
x
)

=

L

.
II. lim
x
→
c

f
(
x
)

=

L

=
⇒
lim
x
→
c
f
(
x
L.
1.
I only
correct
2.
both I and II
3.
neither I nor II
4.
II only
Explanation:
004
10.0 points
A function
f
is deFned piecewise for all
x
±
= 0 by
f
(
x
3+
1
2
x,
x <

2
,
5
2
x,
0
<

x
 ≤
2
,
5+
x

1
2
x
2
,
x >
2
.
By Frst drawing the graph of
f
, determine all
the values of
a
at which
lim
x
→
a
f
(
x
)
exists, expressing your answer in interval no
tation.
1.
(
∞
,

2)
∪
(

2
,
0)
∪
(0
,
∞
)
2.
(
∞
,

2)
∪
(

2
,
0)
∪
(0
,
2)
∪
(2
,
∞
)
3.
(
∞
,
0)
∪
(0
,
∞
)
4.
(
∞
,
2)
∪
(2
,
∞
)
5.
(
∞
,
0)
∪
(0
,
2)
∪
(2
,
∞
)
6.
(
∞
,

2)
∪
(

2
,
∞
)
correct
7.
(
∞
,

2)
∪
(

2
,
2)
∪
(2
,
∞
)
Explanation:
The graph of
f
is
24

2

4
2
4

2

4
and inspection shows that
lim
x
→
a
f
(
x
)
will exist only for
a
in
(
∞
,

2)
∪
(

2
,
∞
)
.