MAC 2233 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. You should review problems from
practice exams, problem sets, projects, and lecture as well.
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
→∞
4
x

3
x
3
x
2

1
lim
x
→
2
1
2

1
x
2

2
2

x
lim
x
→
2
+
x
2
+ 8
x

20

2

x

2. Find an equation of a line
L
that passes though (2,2) and is perpendicular to the line repre
sented by the equation
2
y

8
x
= 5
.
3. Find the intercepts of the line
L
from problem 2. Suppose
y
represents the number of units of
a product (in thousands) that will sell at price
x
dollars. Interpret the slope and
x
 intercept
of the line in terms of dollars and units sold.
4. Factor the negative exponents and then find all intercepts of the graph of the function:
f
(
x
) =
x
(3
x
+ 4)

1
2

(3
x
+ 4)
1
2
5. Solve the inequality:
8

4
x
2
x
≥
6
6. Find the domain of each of the following functions:
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 Spring '08
 Smith
 Calculus, Sets, Supply And Demand, lim, Continuous function, average global temperature

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