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What is the correct answer?

4

What is the integral of vx with respect to x?

A. (2/3)x^(3/2) + C

B. (1/2)x^(3/2) + C

C. 2vx + C

D. x^(3/2) + C

Correct Answer :

B. (1/2)x^(3/2) + C


Related Questions

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4

What is the volume of the region bounded by the surfaces z = x^2 + y^2 and z = 4 - x^2 - y^2?

A. 4p

B. 8p

C. 16p

D. 32p

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4

The area between the curve y = x^2 and the x-axis from x = 0 to x = 2 is equal to:

A. 2

B. 4

C. 8/3

D. 16/3

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4

The integral ?(0 to 1) x^3 dx is equal to:

A. 0

B. 1/4

C. 1/3

D. 1/2

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4

If a plane is defined by the equation 2x - 3y + z = 7, what is the normal vector to the plane?

A. <2, -3, 1>

B. <3, 2, -1>

C. <1, 3, -2>

D. <-2, 3, -1>

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4

The solution to the logistic differential equation dy/dx = ky(1 - y) is often used to model population growth. What happens to the population when y = 1?

A. The population is increasing.

B. The population is decreasing.

C. The population is zero.

D. The population remains constant.

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4

The function P(t) represents the population of a city at time t. What does ?(a to b) P(t) dt represent?

A. The average population of the city on [a, b]

B. The change in population of the city from time a to time b

C. The rate of population growth at time a

D. The population of the city at time b

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4

In parametric equations, what do the variables x and y depend on?

A. Time t

B. Angle ?

C. Radius r

D. Both a and b

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4

If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?

A. 25

B. 33

C. 41

D. 49

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4

What is a vector?

A. A point in space

B. A scalar quantity

C. A quantity with magnitude and direction

D. A constant value

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4

What is the integral of 3x^2 with respect to x?

A. x^3 + C

B. x^2 + C

C. x^3/3 + C

D. 3x + C

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4

What is the directional derivative of the function f(x, y) = x^2 + y^2 at the point (1, 2) in the direction of the vector v = <3, 4>?

A. 1

B. 2

C. 3

D. 4

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4

What is the distance between the points A(2, -1, 3) and B(4, 3, -2)?

A. v42

B. v30

C. v29

D. v35

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4

What is the area under the curve y = sin(x) from x = 0 to x = p?

A. 0

B. 1

C. p

D. 2p

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4

Which of the following is an exact differential equation?

A. dy/dx = 2xy

B. dy/dx = x^2 + y^2

C. dy/dx = e^x

D. dy/dx = y^2 - x^2

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4

What is the limit of f(x) as x approaches 3 for the function f(x) = 2x + 1?

A. 5

B. 6

C. 7

D. 8

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4

What is the derivative of the constant function f(x) = 7?

A. 0

B. 1

C. 7

D. -7

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4

What is the equation of a sphere with center (1, -2, 3) and radius 4?

A. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4

B. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16

C. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4

D. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16

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4

What is the derivative of ln(x) with respect to x?

A. 1/x

B. 1

C. x

D. 0

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4

What is the general solution to the differential equation dy/dx = 3x^2?

A. y = x^3 + C

B. y = 3x + C

C. y = x^3/3 + C

D. y = 3x^3 + C

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4

If a car's speed is decreasing over time, what can you conclude about its acceleration?

A. The acceleration is positive.

B. The acceleration is negative.

C. The acceleration is zero.

D. Nothing about the acceleration can be determined.

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4

If f(x) = x^3 + 2x^2 - 5x + 1, what is f''(x)?

A. 3x^2 + 4x - 5

B. 6x + 4

C. 6x^2 + 4

D. 3x^2 + 4

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4

What is the antiderivative of e^(2x) with respect to x?

A. e^(2x) + C

B. (1/2)e^(2x) + C

C. (1/2)e^(2x^2) + C

D. (1/4)e^(2x) + C

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4

What is the derivative of the vector-valued function r(t) = <2t, t^2, 3t + 1> with respect to t?

A. <2, 2t, 3>

B. <2, 2t, 3t + 1>

C. <2t, 2t^2, 3>

D. <0, 0, 0>

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4

What is the equation of the tangent plane to the surface z = 2x^2 + 3y^2 at the point (1, -1, 5)?

A. z = 2x - 3y + 5

B. z = 2x + 3y - 5

C. z = 2x - 3y - 5

D. z = 2x + 3y + 5

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4

Which of the following limits does not exist?

A. lim (x -> 0) (1/x)

B. lim (x -> 2) (x^2 - 4)/(x - 2)

C. lim (x -> 1) (x^2 - 1)/(x - 1)

D. lim (x -> 3) (1/x^2)

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4

What is the equation of the polar curve r = 2cos(?)?

A. A circle centered at the origin

B. A cardioid

C. A parabola

D. A line

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4

What is the integral of vx with respect to x?

A. (2/3)x^(3/2) + C

B. (1/2)x^(3/2) + C

C. 2vx + C

D. x^(3/2) + C

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4

What is the limit of (sin x) / x as x approaches 0?

A. 1

B. 0

C. -1

D. Undefined

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4

If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?

A. The quantity is 10 at t = 4.

B. The quantity is 0 at t = 4.

C. The quantity is increasing at t = 4.

D. Nothing about the quantity at t = 4 can be determined.

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4

Which test can be used to determine the convergence of a series when its terms are all positive?

A. Alternating Series Test

B. Ratio Test

C. Integral Test

D. Comparison Test