MA 22400
Final Exam Practice Problems
The Formula Page (available on the course web site) will be attached to the fnal exam.
1. Evaluate
i p
2
x

√
x
P
dx.
A. ln

x
 
2
√
x
+
C
B.

2
x
2

1
2
x
1
/
2
+
C
C. 2 ln

x
 
2
x
3
/
2
3
+
C
D.

2
x
2

2
x
3
/
2
3
+
C
E. 2 ln

x
 
1
2
√
x
+
C
2. Evaluate
i
1
(3
x

1)
4
dx
.
A.

12
(3
x

1)
5
+
C
B.

1
9(3
x

1)
3
+
C
C.
1
(3
x

1)
3
+
C
D.

1
3(3
x

1)
3
+
C
E.

4
(3
x

1)
5
+
C
3. Evaluate
i
e
3
−
2
x
dx.
A.

2
e
3
−
2
x
+
C
B.

1
2
e
3
−
2
x
+
C
C.
e
4
−
2
x
4

2
x
+
C
D.
1
3
e
3
−
2
x
+
C
E.
e
3
−
2
x
3

2
x
+
C
4. Find a ±unction
f
whose tangent line has slope
x
√
5

x
2
±or each value o±
x
and whose graph
passes through the point (2,10).
A.
f
(
x
) =

1
3
(5

x
2
)
3
/
2
B.
f
(
x
) =
2
3
(5

x
2
)
3
/
2
+
28
3
C.
f
(
x
) =
1
3
(5

x
2
)
3
/
2
+
29
3
D.
f
(
x
) =

1
3
(5

x
2
)
3
/
2
+
31
3
E.
f
(
x
) =
3
2
(5

x
2
)
3
/
2
+
17
2
5. Evaluate
i
x
ln(
x
2
)
dx
.
A.
1
2
x
2
ln
x
2

1
2
x
2
+
C
B.
1
2
x
2
ln
x
2

1
2
x
+
C
C.
1
2
x
2
ln
x
2

1
6
x
3
+
C
D.
x
ln
x
2
+
1
x
+
C
E.
1
2
x
2
ln
x

1
2
x
2
+
C
6. The area o± the region bounded by the curves
y
=
x
2
+ 1 and
y
= 3
x
+ 5 is
A.
125
6
B.
56
3
C.
27
2
D.
25
6
E.
32
3
7. Find the average value o±
f
(
x
) =
x
2
over the interval 1
≤
x
≤
4
.
A.
17
2
B.
15
2
C. 21 D.
65
3
E. 7
8. A calculator manu±acturer expects that
x
months ±rom now consumers will be buying 1,000
calculators a month at a price o± 20+3
√
x
dollars per calculator. What is the average revenue
the manu±acturer can expect ±rom the sale o± calculators over the next 4 months?
A. $8,000 B. $16,000 C. $24,000 D. $96,000 E. $6,500
9. I±
f
(
x, y
) = (
xy
+ 1)
2

r
y
2

x
2
, evaluate
f
(

2
,
1).
A. 1 B. 1

√
5 C. Not defned D.

1

√
5 E.

1

√
3
10. A paint store carries two brands o± latex paint. Sales fgures indicate that i± the frst brand
is sold ±or
x
1
dollars per gallon and the second ±or
x
2
dollars per gallon, the demand ±or the
frst brand will be
D
1
(
x
1
, x
2
) = 100 + 5
x
1

10
x
2
gallons per month and the demand ±or the
second brand will be
D
2
(
x
1
, x
2
) = 200

10
x
1
+ 15
x
2
gallons per month. Express the paint
store’s total monthly revenue,
R
, as a ±unction o±
x
1
and
x
2
.
A.
R
=
x
1
D
1
(
x
1
, x
2
) +
x
2
D
2
(
x
1
, x
2
)
B.
R
=
D
1
(
x
1
, x
2
) +
D
2
(
x
1
, x
2
)
C.
R
=
D
1
(
x
1
, x
2
)
D
2
(
x
1
, x
2
) D.
R
=
x
2
D
(
x
1
, x
2
)+
x
1
D
2
(
x
1
, x
2
) E.
R
=
x
1
x
2
+
D
1
(
x
1
, x
2
)
D
2
(
x
1
, x
2
)
1