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Material Type: Quiz; Class: Calculus I; Subject: Mathematics; University: East Georgia College; Term: Fall 2007;
Typology: Quizzes
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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.
Find the second derivative.
Find y ′.
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.
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)
= 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.
x6^ +x6e A) 6 7
x
x
x-
x
Find the derivative of the function.
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 v
at x = 1
Solve the problem.
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.
Solve the problem.
= 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.
sin 6t + 11
C) dq dt = - sin 3 6t + 11
D) dq dt = - 1 2 6t + 11
sin 6t + 11
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
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
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.
Use implicit differentiation to find dy/dx.
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
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.
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.
x
2x + 8
x
Find the derivative of y with respect to x, t, or θ, as appropriate.
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.
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.
B) 18 x 1 + (9x2^ - 4)
C) -^18 x (^1) - (9x2^ - 4)^
(^1) + (9x2^ - 4)
A) -^2 x x4^ - 1
1 + x^
C) - 2x
(^1) - x^
x (^1) - x
Solve the problem.
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