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MAC 2311
4pm, Jan 30, 2009
Exam I
Prof. S. Hudson
1) [30 points] Compute each limit:
a) lim
x
→
2
q
2
x
2

8
x

2
=
b) lim
x
→
+
∞
tan

1
(
x
) =
c) lim
x
→
+
∞
√
x
2

1

x
=
2) [20pt] Short answer problems:
a) Find all values of
θ
(in radians) that satisfy the equation cos(
θ
) =

1
√
2
b) Solve
x
2

4
x
+ 3
<
0.
3) (20pts) Answer True or False. You do not have to explain.
a) tan(
π/
2 +
x
) is continuous at every point in the interval (0
,π
).
b) If lim
x
→
2
f
(
x
) exists, then lim
x
→
2
+
f
(
x
) exists.
c) If
x
is a number so that

x

2

<
1, then

x

4

<
5.
d)
∀
± >
0
,
∃
δ >
0
,δ
+
± < .
001.
e) If
f
(1) = 1 and
f
(3) = 3, and
f
is continuous, then
f
(
x
) = 2 for some
x
in (1
,
3).
f) For
f
(
x
) =
x
2
+ 1, the slope of every secant line is positive.
g) The domain of
f
+
g
is the same as the domain of
fg
.
h) The derivative of tan

1
(
x
) at
x
= 1 is positive.
i) If
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