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Math 1540 Quiz 2 Practice Fall 2007
Name: Last ____________________, First ____________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the derivative.
- y = 5x^2 + 11x + 4x-^3 A) 10x + 11 + 12x-^4 B) 5x + 4x-^4 C) 10x - 12x-^4 D) 10x + 11 - 12x-^4
Find the second derivative.
- y (^) = 4x^2 + 12x (^) + 5x-^3 A) (^8) - 60x-^5 B) 8x (^) + 12 - 15x-^4 C) (^8) + 60x-^5 D) (^8) + 60x-^1
Find y ′.
- y = (5x - 3)(5x^3 - x^2 + 1) A) 75x^3 + 60x^2 - 20x + 5 B) 100x^3 - 60x^2 + 6x + 5 C) 100x^3 - 20x^2 + 60x + 5 D) 25x^3 + 20x^2 - 60x + 5
- y (^) = x (^) + 1 x
x (^) - 1 x
A) 2x + 2 x^
B) 2x + 1 x^
C) 2x + 1 x^
D) 2x - 1 x
Find the derivative of the function.
- g(x) (^) = x
x2^ + 6x
A) g ′(x) (^) = 4x
(^3) + 18x (^2) + 10x (^) + 30 x2(x (^) + 6)^
B) g ′(x) (^) = x
(^4) + 6x (^3) + 5x (^2) + 30x x2(x (^) + 6)
C) g ′(x) (^) = 2x
(^3) - 5x (^2) - 30x x2(x (^) + 6)^
D) g ′(x) (^) = 6x
(^2) - 10x (^) - 30 x2(x (^) + 6)
- y = x^8 e-x A) dy dx
= 8x9e-x^ - x8e-x^ B) dy dx
= 8x7e-x^ - x8e-x
C) dy dx =^
8x7e-x^ + x8e-x^ D) dy dx =^
8x9e-x^ + x8e-x
Find the derivative.
- y = 3x2e-x A) 3xe-x(x + 2) B) 3xe-x(2 - x) C) 6xe-x(1 - x) D) 3xex(2 - x)
- y =
x6^ +x6e A) 6 7
x
x
C) 6
x-
x
Find the derivative of the function.
- p = q
2q
q^7 + 6 q
A) dp dq
q16^ + 18q8^ + 30q9^ - 24 q^
B) dp dq
q12^ - 24 q
C) dp dq
q12^ + 10q4^ + 18q5^ - 24 q^
D) dp dq
q12^ + 2q4^ + 3q5^ + 24 q
Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative.
- u(1) = 5 , u ′(1) = - 7 , v(1) = 6 , v ′(1) = - 2. d dx
u v
at x = 1
A) - 8
B) - 16
C) - 13
D) - 8
Solve the problem.
- Find an equation for the tangent to the curve y (^) = 8 x x2^ + 1
at the point (1, 4).
A) y (^) = 0 B) y (^) = x (^) + 4 C) y (^) = 4 D) y (^) = 4 x
The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.
- s = 3t^2 + 3t + 3, 0 ≤ t ≤ 2 Find the body's speed and acceleration at the end of the time interval. A) 9 m/sec, 2 m/sec^2 B) 18 m/sec, 6 m/sec^2 C) 15 m/sec, 12 m/sec^2 D) 15 m/sec, 6 m/sec^2
Solve the problem.
- At time t, the position of a body moving along the s-axis is s = t^3 - 27t^2 + 240t m. Find the body's acceleration each time the velocity is zero. A) a(10) = 6 m/sec^2 , a(8) = - 6 m/sec^2 B) a(20) = 120 m/sec^2 , a(16) = 20 m/sec^2 C) a(10) = 0 m/sec^2 , a(8) = 0 m/sec^2 D) a(10) = - 6 m/sec^2 , a(8) = 6 m/sec^2
- At time t ≥ 0, the velocity of a body moving along the s-axis is v = t^2 - 8t + 7. When is the body moving backward? A) (^0) ≤ t (^) < 1 B) (^1) < t (^) < 7 C) (^0) ≤ t (^) < 7 D) t (^) > 7
- s (^) = t^2 - cos t (^) + 4et A) ds dt
= 2t - sin t + 4et^ B) ds dt
= 2t + sin t - 4et
C) ds dt = 2t + sin t + 4et^ D) ds dt = t + sin t + 4et
Find the derivative of the function.
- q = cos 6t + 11 A) dq dt = - sin 6t + 11 B) dq dt = - 3 6t + 11
sin 6t + 11
C) dq dt = - sin 3 6t + 11
D) dq dt = - 1 2 6t + 11
sin 6t + 11
- q = 16r - r
A) dq dr = 1 2 16 - 5r^
B) dq dr = 1 2 16r - r
C) dq dr
= -^ 5r
16r - r^
D) dq dr
= 16 -^ 5r
2 16r - r
- h(x) = cos x 1 + sin x
A) h′(x) = 5 cos x 1 + sin x
B) h′(x) = -^ 5 cos
(^4) x (1 + sin x)
C) h′(x) = - 4 sin x cos x
cos x 1 + sin x
D) h′(x) = - 5 sin x cos x
- f(x) = cos (8x + 6)-1/
A) f ′(x) = - sin -^4 (8x + 6)3/^
B) f ′(x) = 4 sin (8x^ +^ 6)
(8x + 6)3/
C) f ′(x) = -^ sin (8x^ +^ 6)
2(8x + 6)3/^
D) f ′(x) = - sin (8x + 6)-1/
Find the value of (f ∘ g)′ at the given value of x.
- f(u) = u^2 , u = g(x) = x^5 + 2, x = 0 A) - 30 B) 15 C) 4 D) 0
Use implicit differentiation to find dy/dx.
- cos xy + x^4 = y^4
A) 4x
(^3) - y sin xy 4y3^ + x sin xy
B) 4x
(^3) - x sin xy 4y^
C) 4x
(^3) + y sin xy 4y3^ - x sin xy
D) 4x
(^3) + x sin xy 4y
- xy (^) + x (^) + y (^) = x^2 y^2
A) 2xy
(^2) + y 2x2y (^) - x
B) 2xy
(^2) + y (^) + 1
C) 2xy
(^2) - y (^) - 1
D) 2xy
(^2) - y 2x2y (^) + x
Find the formula for df-^1 /dx.
- f(x) = x^7 /^3 A) x^4 /^7 B) 3 7
x-4/7^ C) 7 3
x4/3^ D) x^3 /^7
Find the derivative of y with respect to x, t, or θ, as appropriate.
- y = ln 8x^2 A) 2x x2^ + 8
B) 2
x
C) 1
2x + 8
D) 16
x
Find the derivative of y with respect to x, t, or θ, as appropriate.
- y (^) = e(4^ x^ +^ x^5 ) A) 2 x
- 5x4^ e(4^ x^ +^ x5)^ B) 4 x + 5x4) e(4^ x^ +^ x^5 )
C) (4 x + 5x^4 ) ln (4 x + x^5 ) D) e(2^ x^ +^ 5x^4 )
Find the derivative of y with respect to x, t, or θ, as appropriate.
- y = ln x x
A) 1 -^5 ln x x^
B) 1 +^5 ln x x^
C) 5 ln x^ -^1 x^
D) 1 -^5 ln x x
Find the derivative of y with respect to x.
- y = cos-^1 (9x^2 - 4) A) 18 x 1 - (9x2^ - 4)^
B) 18 x 1 + (9x2^ - 4)
C) -^18 x (^1) - (9x2^ - 4)^
D) 9
(^1) + (9x2^ - 4)
- y = sin-^1 x
A) -^2 x x4^ - 1
B) -^2
1 + x^
C) - 2x
(^1) - x^
D) -^2
x (^1) - x
Solve the problem.
- V = 4 3
πr3, where r is the radius, in centimeters. By approximately how much does the volume of a
sphere increase when the radius is increased from 3.0 cm to 3.1 cm? (Use 3.14 for π.) A) 11.5 cm^3 B) 11.3 cm^3 C) 0.4 cm^3 D) 11.1 cm^3
Answer Key
Testname: MATH 1540 QUIZ 2 PRACTICE
1) D
2) C
3) B
4) A
5) D
6) B
7) B
8) C
9) C
10) A
11) C
12) D
13) A
14) B
15) A
16) D
17) B
18) A
19) D
20) C
21) B
22) D
23) B
24) B
25) D
26) A
27) C
28) B
29) B
30) A
31) D
32) C
33) A
34) A
35) B
36) B
37) D
38) C
39) D
40) B
