Review – Exam 1
*
This is intended to be a tool to help you review some of the material that could
appear on the exam.
It is not inclusive of all topics discussed in lecture.
1. Evaluate the following limits:
lim
x
→
2
√
x
2
+ 6
x

4
x

2
lim
x
→
3

x
2
+ 3
x

18
x
2

9
lim
x
→
3
+
x
2
+ 3
x

18
x
2

9
lim
x
→
0
+
√
x
sin(
1
x
)
lim
x
→
2
1
2

1
x
2

2
2

x
lim
x
→
2
+
x
2
+ 8
x

20

2

x

2. Given that sin(
x
) =
8
17
, cos(
y
) =
4
5
,
x
is an angle in Quadrant I, and
y
is
an angle in Quadrant IV, evaluate csc(
y
) and tan(
x
+
y
) .
3. Suppose
f
,
g
, and
h
are functions such that
lim
x
→
1
h
(
x
) = 4 , lim
x
→
2
f
(
x
) =

2 ,
and
lim
x
→
2

g
(
x
) =
1
2
.
Evaluate
lim
x
→
1
+
h
(
fg
)(

2
x
)
( 1

p
h
(
x
) )
2
4. Solve for
x
in [

π, π
]:
tan(
x
)

sin(2
x
) = 0
5. Solve the inequality:
8

4
x
2
x
≥
6
6. Find the domain of the following functions:
f
(
x
) =
r
x
2

8
x
g
(
x
) =
x
2
x
2

4
x
h
(
x
) =
x
2

ln(
x
)
7. If
f
(
x
) =
1
√
2 +
x
and
g
(
x
) = 1

x
2
, find
g
(
f
(
x
) ) and its domain.
8. Determine
r
and
s
so that the piecewise defined function below is continuous
on the real line.
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 Fall '08
 ALL
 Calculus, Limits, lim, Continuous function, Inverse function, 2 seconds, 10gram

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