Math 1110 (Fall 2009)
Prelim 1 (09/29/2009)
1
Question 1. (20 points)
Please answer the following questions about the function
f
(
x
)
whose
graph is shown in the figure below.
y=0
y=1
x=0
x=1
(a) Is
f
(
x
)
a onetoone function? Why or why not?
Answer to 1a.
No.
(b) On which intervals between

5
and
5
is
f
(
x
)
increasing?
Answer to 1b.
[
5,

1
]
and
[
2, 4
)
.
(c) For which values of
c
is lim
x
→
c
f
(
x
) = 
1
?
Answer to 1c.
c
=
0
.
(d) For which values of
c
is lim
x
→
c
+
f
(
x
)
6
=
lim
x
→
c

f
(
x
)
?
Answer to 1d.
c
= 
1
and
c
=
2
.
(e) At which values
c
between

5
and
5
is
f
(
x
)
continuous?
Answer to 1e.
Everywhere except
c
= 
1, 2, 4
.
Question 2. (18 points)
Please evaluate the following expressions, if they exist, or indicate that
they do not. If you use a theorem or a fact about limits to help get an answer, be sure to reference
it in your solution. If a limit does not exist, indicate in what way it fails to exist. For example, “the
onesided limits disagree.”
(a) lim
x
→
1
x
2

6x
+
5
2x
2

2
= 
1
(b)
lim
x
→

∞
x
2

6x
+
5
2x
2

2
=
1
2
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Math 1110 (Fall 2009)
Prelim 1 (09/29/2009)
2
(c)
lim
x
→

1
x
2

6x
+
5
2x
2

2
=
DNE
(does not exist)
(d) log
a
(
a
10
) 
log
a
(
1
) =
10
(e) lim
x
→
0
ln
sin
(
√
e x
)
x
=
1
2
(f) If lim
x
→
2
f
(
x
) =
10
and lim
x
→
2
g
(
x
) = 
5
, then lim
x
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 '06
 MARTIN,C.
 lim

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