MATH 1325 TEST 1 REVIEW FALL 2015
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the limit, if it exists.
6x + 5
1) Find: lim
x -1 5x - 6
A) -11
1)
B) 1
C)
2) Given lim f(x) = -2 and lim g(x) = 5, find lim
x 4
x 4
x 4
A) -
3) Find:
7
8
lim
x 3
B) -
x2 - 9
+
x-3
A) 2
1
11
D) -
1
11
[g(x) - f(x)]
.
- 4 f(x)
3
8
C)
7
8
2)
D)
3
8
x2 + 7
3)
B) 10
C) 3
D) Does not exist
Solve the problem.
4) A company training program determines that, on average, a new employee can do P(x) pieces of
90 + 60x
work per day after s days of on-the-job training, where P(x) =
. Find lim P(x).
x+5
x 5
A) 42
B) 105
C) 30
Find the instantaneous rate of change for the function at the value given.
5) Find the instantaneous rate of change for the function x2 + 4x at x = 6.
A) 10
B) 60
C) 12
Find the equation of the tangent line to the curve when x has the given value.
6) f(x) = 2- x2 ; x = 3
A) y = -6x + 11
B) y = 3x + 11
C) y = 6x - 11
List the x-values in the graph at which the function is not differentiable.
7)
A) x = -3, x = 0, x = 3
C) x = -3, x = 3
B) x = -2, x = 2
D) x = -2, x = 0, x = 2
1
4)
D) Does not exist
D) 16
D) y = -2x
5)
6)
7)
Solve the problem.
8) An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given
by f(t) = 9t3 - 9t2 + t + 7. Find the velocity at three seconds.
A) 192 feet per second
C) 190 feet per second
B) 109 feet per second
D) 197 feet per second
9) If an object moves along a line so that it is at y = f(x) = 2x2 - 7x - 6 at time x (in seconds), find the
instantaneous velocity function v = f'(x).
A) 2x2 - 7
B) 4x - 7
C) 4x2 - 7
D) 2x - 7
Find the equation of the tangent line to the curve when x has the given value.
10) f(x) = -4- x2 ; x = 4
A) y = 8x - 12
Differentiate.
11) Find
B) y = -2x
C) y = 4x + 12
D) y = -8x + 12
dy
x2 - 3x + 2
for y =
.
dx
x7 - 2
dy - 5x8 + 18x7 - 13x6 - 4x + 6
=
dx
2
(x7 - 2)
B)
dy - 5x8 + 18x7 - 14x6 - 3x + 6
=
dx
2
(x7 - 2)
C)
dy - 5x8 + 19x7 - 14x6 - 4x + 6
=
dx
2
(x7 - 2)
D)
dy - 5x8 + 18x7 - 14x6 - 4x + 6
=
dx
2
(x7 - 2)
A)
17
(2x - 7)2
9)
10)
11)
A)
12) Find f'(t) for f(x) =
8)
2x - 7
.
3x - 2
12)
B)
17
C) -
(3x - 2)2
17
(3x - 2)2
D) -
17
(2x - 7)2
Solve the problem.
13) According to one theory of learning, the number of items, w(t), that a person can learn after t hours
of instruction is given by:
3
w(t) = 15 t2 ,
0 t 64
Find the rate of learning at the end of eight hours of instruction.
A) 20 items per hour
B) 5 items per hour
C) 60 items per hour
D) 45 items per hour
13)
Differentiate.
14) Find f'(x) for f(x) = (2x - 4)(2x3 - x2 + 1).
A) f'(x) = 16x3 - 10x2 + 30x + 2
B) f'(x) = 12x3 + 30x2 - 10x + 2
D) f'(x) = 4x3 - 10x2 - 30x + 2
C) f'(x) = 16x3 - 30x2 + 8x + 2
2
14)
Solve the problem.
15) A publishing company has published a new magazine for young adults. The monthly sales S (in
800t
thousands) is given by S(t) =
, where t is the number of months since the first issue was
t+ 2
15)
published. Find S(3) and S'(3) and interpret the results.
A) At three months, the monthly sales are $480,000 and decreasing at 64,000 magazines per
month.
B) At three months, the monthly sales are $480,000 and increasing at 64,000 magazines per
month.
C) At three months, the monthly sales are $2,400,000 and increasing at 800,000 magazines per
month.
D) At three months, the monthly sales are $2, 400,000 and increasing at 64,000 magazines per
month.
Provide an appropriate response.
16) Find f'x for f(x) =
(3x + 4)2
. Do not simplify.
x3 - x2 + 3x
16)
A)
(3x + 4)2(3x2 - 2x + 3) - 6(x3 - x2 + 3x)(3x + 4)
2
(x3 - x2 + 3x)
B)
6(x3 - x2 + 3x)(3x + 4) - (3x + 4)2 (3x2 - 2x + 3)
(3x + 4)4
C)
6(x3 - x2 + 3x)(3x + 4) - (3x + 4)2 (3x2 - 2x + 3)
(x3 - x2 + 3x)2
D)
(3x + 4)2(3x2 - 2x + 3) - 6(x3 - x2 + 3x)(3x + 4)
(3x + 4)4
17) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4x2 - 5x
+ 10. Find the marginal profit at x = 5.
A) $35
B) $32
C) $45
D) $15
17)
Differentiate.
18) Find f'(t) for f(x) = (2x - 2)(3x3 - x2 + 1)
A) f'(x) = 18x3 + 24x2 - 8x + 2
B) f'(x) = 6x3 + 8x2 - 24x + 2
C) f'(x) = 24x3 - 24x2 + 4x + 2
18)
D) f'(x) = 24x3 - 8x2 + 24x + 2
Solve the problem.
19) Suppose the demand for a certain item is given by D(p) = -3p2 + 4p + 8, where p represents the
price of the item. Find D'(p), the rate of change of demand with respect to price.
A) D'(p) = -3p2 + 4
B) D'(p) = -6p + 4
C) D'(p) = -6p2 + 4
D) D'(p) = -3p + 4
19)
Find f (x).
20) f(x) = -7 ln x - x4 + 2
7
A) - - 4x3
x
1
- 4x3
B) 7x
7
C) - - 4x
x
3
7
D) - 4x3
x
20)
Find the derivative.
21) Find f'(x) for f(x) = (8x - 9)-4 .
4
4
A) B) 5
(8x - 9)
(8x - 9)3
22) Find
A)
d
d
C) -
32
(8x - 9)5
D) -
32
(8x - 9)3
4
22)
5
( 2 + 3)
- 40
( 2 + 3)
6
21)
B)
40
( 2 + 3)
C)
6
- 40
( 2 + 3)
6
D)
- 40
5
( 2 + 3)
Find f (x).
23) f(x) = ln x5 - 9ex + 3x2
5
- 9ex + 6
A)
x4
C)
5
- 9xex-1 + 6x
x
24) f(x) = ln x9
1
A)
9x
D)
B)
25) f(x) = 9ex - 6x + 2
A) 9ex - 4
9
C)
x8
B) 9xex-1 - 6
5
- 9ex + 6x
x
24)
9
x
D) 9 ln x8
C) 9ex - 6x
Find the instantaneous rate of change for the function at the value given.
26) Find the instantaneous rate of change for the function x2 + 9x at x = 5.
A) 70
23)
5
B) - 9ex + 3x
x
B) 19
C) 14
D) 9ex - 6
D) 10
25)
26)
Find the derivative.
27) Find:
dy 8 7
8x - 10
dx
27)
7
A) 8 8x7 - 10
C) 448x6
7
B)
8x7 - 10
D)
56x6
(8x7 - 10)7/8
7x6
(8x7 - 10)7/8
Provide an appropriate response.
28) The revenue (in thousands of dollars) from producing x units of an item is modeled by
R(x) = 5x - 0.0005x2. Find the marginal revenue at x = 1000.
A) $4.50
B) $104.00
C) $10,300.00
4
D) $4.00
28)
Answer Key
Testname: 1325 TEST 1 REVIEW FALL 2015
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C
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D
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