Math 103-001 – Rimmer
Practice Problems for Exam 3 taken from old midterms
Fall 2011
1. A closed rectangular box with a volume of 4 ft.3 is to be constructed. The length of the base of the
box will be twice as long as its width. The material for the top and bottom of the box costs 30 cents per
square foot, and the material for the sides of the box costs 20 cents per square foot. Find the
dimensions of the least expensive box that can be constructed. Answers are in the
length × width × height order and all dimensions are in feet.
1
2
2
e) 6 × 3 ×
9
a) 4 × 2 ×
1
2
1 1
g) × × 32
2 4
b) 2 × 1× 2
c) 1× × 8
5 8
2 25
f) 5 × ×
d) 8 × 4 ×
1
8
h) None of these
2. An open box is made from an 8 inch × 8 inch piece of cardboard by cutting equal squares from each
corner and folding up the sides. What size squares should be cut out to create a box with maximum
volume?
3. If f ′′ ( x ) = 6 x 2 + 6 x + 2 with f ( −1) =
a)
b)
c)
d)
32
33
36
16
e)
f)
g)
h)
1
and f ′ ( −1) = 2, find f ( 2 ) .
2
20
24
25
29
9
4. Use the graph of f shown in the figure to evaluate
∫ f ( x ) dx
−4
A) 2
B)
3
2
C)
5
2
D)
−9
2
E)
−7
2
F)
−1
2
G)
−3
2
H)
−5
2
Math 103-001 – Rimmer
Practice Problems for Exam 3 taken from old midterms
Fall 2011
5. Let
x
g ( x ) = ∫ te t dt .
1
Find
g ′′ ( 4 ) .
B) 3e 2
A) 2
C) 2e2
D) 0
E)
1
2
e2
F) e 2
3
2
G)
e2
H) 1
6. Let
9
5
x −1
L=∫
dx and M = ∫ 2 x − 1dx. Find L − M .
x
4
1
A) −2
B) 2
58
3
C)
D)
5
3
E)
4
3
F)
2
3
G) 1
H)
1
2
7. Compute the limit
e− x − cos x + tan x
lim 2
x →0 3 x + tan x − sin x
A)
1
3
B)
1
6
C)
1
2
D)
1
4
E)
1
8
F)
2
3
G) 1
H) does not exist
8. Compute the limit
(
lim x 2 + e x
x →∞
A)
1
2
B)
)
1
x
e
C) e 2
D) e
E) 0
F) ∞
G) 1
H) does not exist
Answers:
1. B
2. 4/3” X 4/3”
3. H
4. H
5. C
6. B
7. A
8. D