MAC2233 Chapter 2 Review
1. For the function
f
(
x
) =
x
2

3
x

4 state the domain and evaluate the
function at
x
=

1
,
0
, a
+
h.
2. For the function
y
=
1
t
2
+
t

2
state its domain as well as the dependent
and independent variables and evaluate the function at
t
=

3
,
3
.
3. For the function
g
(
x
) =

2
x
+ 5
,
x
≤ 
3
0
,

3
< x <
1
x
3
,
1
≤
x
evaluate the function at
x
=

1
,
1
,
5
.
4. Given
f
(
x
) =
x
2
+ 1 and
g
(
x
) =
√
x
+ 1 ﬁnd
f
+
g, f

g, fg, f/g,
g
◦
f, f
◦
g
and state the domain for each.
5. Find and simplify
f
(
a
+
h
)

f
(
a
)
h
where
f
(
x
) = 2
x
2

x
+ 1.
6. A manufacturing company has a monthly ﬁxed cost of $100
,
000 and
variable cost in dollars of
V
(
x
) = 0
.
000003
x
3

0
.
03
x
2
+ 200
x
where
x
denotes the number of units manufactured per month. The revenue
for the company is given in dollars by
R
(
x
) =

0
.
1
x
2
+ 500
x.
Find the proﬁt function for the company and the proﬁt when 1500 units are
produced and sold each month.
7. A demand curve is given by
p
=
d
(
x
) = 60

2
x
2
and a supply curve
is given by
p
=
s
(
x
) =
x
2
+ 9
x
+ 30 where
x
is the quantity demanded in
thousands and
p
is the unit price in dollars. Find the equilibrium quantity
and the equilibrium price.
8. Evaluate the following limits:
f
(
x
) =
x
+ 1
x <
0
5
,
x
= 0
7

x
x >
0
1
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View Full Documenta. lim
x
→
2
f
(
x
) b. lim
x
→
10
f
(
x
) c. lim
x
→
0
f
(
x
) d. lim
x
→
4

f
(
x
)
e. lim
x
→
0
+
f
(
x
)
.
9. Evaluate the following limit: lim
x
→
1
x
+1
x
2
+
x
+1
.
10. Evaluate the following limit: lim
t
→
3
t
3

9
t
t
2

9
.
11. Evaluate the following limit: lim
x
→∞

2
x
4
+3
x
2

1
5
x
2

5
x
+2
.
12. Determine the values of
x
at which the following function is continu
ous:
f
(
x
) =
x
2
+ 2
x

4
x
≤
0
(
x
+ 5)
/
(
x

3)
,
0
< x
≤
4
9
x >
4
.
13. Consider the function
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 Spring '08
 Smith
 Calculus, Supply And Demand, lim, Continuous function, e. lim

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