Practice Test 2- 1325--- Chapter 11
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Compute the instantaneous rate of change of the function at at x = a. f(x) = -7x2 - x, a = -4.
A) -52
B) 56
C) 55
D) 52
2) Use the graph of the function f to find lim f(x).
x→∞
1)
2)
y
10
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10 x
-2
-4
-6
-8
-10
A) does not exist
B) -∞
C) ∞
D) -2
3) A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate
of change of its volume with respect to the length of an edge when the edge is 0.46 mm.
A) 6.35 mm3/mm
B) 0.29 mm3/mm
3
C) 0.6348 mm /mm
D) 63.48 mm3/mm
Find the derivative of the function.
4) f(x) = (x3 - 8)2/3
x
2x
B) fʹ(x) = A) fʹ(x) = 3
3
x3 - 8
x3 - 8
4)
C) fʹ(x) = 2x2
3
D) fʹ(x) = x3 - 8
x2
3
x3 - 8
5) f(x) = (3x - 5)( x + 5)
A) fʹ(x) = 4.5x1/2 - 2.5x-1/2 + 15
C) fʹ(x) = 2x1/2 - 2.5x-1/2 + 15
B) fʹ(x) = 2x1/2 - 5x-1/2 + 15
D) fʹ(x) = 4.5x1/2 - 5x-1/2 + 15
6) y = ln (9x3 - x2)
27x - 2
A)
9x3 - x
27x - 2
B)
9x2 - x
9x - 2
C)
9x2 - x
27x - 2
D)
9x2
2
B) yʹ = 4x + 2
8
C) yʹ = 4x + 2
1
D) yʹ = 4x + 2
5)
6)
7) y = 4x + 2
4
A) yʹ = 4x + 2
3)
7)
1
Find the derivative.
1
8) f(x) = 20x1/2 - x20
2
A) 10x-1/2 - 10x10
5
9) f(x) = x; (x > 0)
6
A) x6/5
5
10)
8)
C) 10x-1/2 - 10x19
B) 10x1/2 - 10x19
D) 10x1/2 - 10x10
9)
6
C) - x-6/5
5
B) 4(4 x)
D)
1 -4/5
x
5
(4x + 5)(3x - 2)
x + 6
10)
A)
12x2+ 144x + 52
x + 6
B)
36x2+ 158x + 32
(x + 6)2
C)
36x2+ 158x + 32
x + 6
D)
12x2+ 144x + 52
(x + 6)2
11) f(x) = ex ln x, x > 0
ex
A)
x
12) y = 11)
ex(ln x + x)
B)
x
ex(x ln x + 1)
C)
x
D) ex ln x
8ex
2ex + 1
A)
8ex
(2ex + 1)3
12)
B)
8ex
(2ex + 1)2
C)
8ex
(2ex + 1)
Find the average rate of change for the function over the given interval.
13) y = 2x between x = 2 and x = 8
3
1
A) 7
B) - C)
10
3
D)
ex
(2ex + 1)2
13)
D) 2
Find functions g and h such that f(x) = g(h(x)).
6
14) f(x) = (5x2 - 6x + 1)3
14)
A) g(x) = 6x-3, h(x) = 5x2 - 6x + 1
6
B) g(x) = , h(x) = (5x2 - 6x + 1)3
x
C) g(x) = x-3, h(x) = 5x2 - 6x + 1
1
D) g(x) = , h(x) = (5x2 - 6x + 1)3
x
Use the properties of limits to evaluate the limit if it exists.
lim x2 - 2x - 15
15)
x→-3
x + 3
A) Does not exist
B) 0
15)
C) 5
2
D) -8
Use the properties of limits to find the indicated limit.
-10x2 + 7x + 19
16) lim x→-∞ -11x2 + 9x + 12
A)
10
11
16)
B) ∞
C) 1
D)
19
12
Decide whether the limit exists. If it exists, find its value.
17) lim f(x)
x→1
A) 0
17)
B) 1
C) 2
D) Does not exist
Use the limit properties to find the following limit.
18) If lim f(x) = 5 and lim g(x) = 18, find lim x→-1
x→-1
x→-1
A) - 13
90
f(x) + g(x)
.
5g(x)
C) -1
B) 1
18)
D)
23
90
Use the given graph to determine the limit, if it exists.
19) lim f(x)
x → 1+
5
19)
f(x)
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
-2
-3
-4
-5
A) 3
B) 4
C) 3
1
2
D) does not exist
Find the equation of the tangent line to the curve when x has the given value.
20) f(x) = x2 + 11x - 15 ; x = 1
A) y = -39x - 80 x 1
C) y = + 20 5
B) y = 13x - 16
3
20)
4x 8
D) y = - + 25 5
Answer Key
Testname: TEST2‐1325‐FALL‐2010
1) C
2) D
3) C
4) C
5) A
6) B
7) B
8) C
9) D
10) D
11) C
12) B
13) C
14) A
15) D
16) A
17) D
18) D
19) A
20) B
4