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40 MCQs with Answer for Quiz 2 - Calculus I | MATH 1540, Quizzes of Calculus

Material Type: Quiz; Class: Calculus I; Subject: Mathematics; University: East Georgia College; Term: Fall 2007;

Typology: Quizzes

Pre 2010

Uploaded on 08/04/2009

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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.
1)
y = 5x
2
+ 11x + 4x
-
3
A)
10x + 11 + 12x
-
4
5x + 4x
-
4
C)
10x - 12x
-
4
D)
10x + 11 - 12x
-
4
1)
Find the second derivative.
2)
y = 4x
2
+ 12x + 5x
-
3
A)
8 - 60x
-
5
8x + 12 - 15x
-
4
C)
8 + 60x
-
5
D)
8 + 60x
-
1
2)
Find
y
.
3)
y = (5x - 3)(5 x
3
- x
2
+ 1)
A)
75x
3
+ 60x
2
- 20x + 5
100x
3
- 60x
2
+ 6x + 5
C)
100x
3
- 20x
2
+ 60x + 5
D)
25x
3
+ 20x
2
- 60x + 5
3)
4)
y = x +
1
x x -
1
x
A)
2x +
2
x3
2x +
1
x3
C)
2x +
1
x2
D)
2x -
1
x2
4)
Find the derivative of the function.
5)
g(x) = x
2
+ 5
x2 + 6x
A)
g(x) = 4x
3
+ 18x
2
+ 10x + 30
x2(x + 6)2
g(x) = x
4
+ 6x
3
+ 5x
2
+ 30x
x2(x + 6)2
C)
g(x) = 2x
3
- 5x
2
- 30x
x2(x + 6)2
D)
g(x) = 6x
2
- 10x - 30
x2(x + 6)2
5)
6)
y = x
8
e
-
x
A)
dy
dx = 8x9e-x - x8e-x
dy
dx = 8x7e-x - x8e-x
C)
dy
dx = 8x7e-x + x8e-x
D)
dy
dx = 8x9e-x + x8e-x
6)
Find the derivative.
7)
y = 3x2e-x
A)
3xe
-
x
(x + 2)
3xe
-
x
(2 - x)
C)
6xe
-
x
(1 - x)
D)
3xe
x
(2 - x)
7)
1
pf3
pf4
pf5
pf8

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Download 40 MCQs with Answer for Quiz 2 - Calculus I | MATH 1540 and more Quizzes Calculus in PDF only on Docsity!

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.

  1. 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.

  1. 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 ′.

  1. 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
  1. 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.

  1. 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)

  1. 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.

  1. y = 3x2e-x A) 3xe-x(x + 2) B) 3xe-x(2 - x) C) 6xe-x(1 - x) D) 3xex(2 - x)
  1. y =

x6^ +x6e A) 6 7

x

  • 6x6e-^1 B) 6 7

x

  • 6x6e-^1

C) 6

x-

  • (^) 6ex6e- (^1) D) 6 7

x

  • (^) 6ex6e- 1

Find the derivative of the function.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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
  1. 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
  1. 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.

  1. 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

  1. 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

  1. 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

  1. 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.

  1. 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.

  1. 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

  1. xy (^) + x (^) + y (^) = x^2 y^2

A) 2xy

(^2) + y 2x2y (^) - x

B) 2xy

(^2) + y (^) + 1

  • 2x2y^ - x^ - 1

C) 2xy

(^2) - y (^) - 1

  • 2x2y^ + x^ + 1

D) 2xy

(^2) - y 2x2y (^) + x

Find the formula for df-^1 /dx.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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)

  1. 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.

  1. 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