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What is the correct answer?

4

If h(x) = e^(2x), what is h'(x)?

A. 2e^(2x)

B. e^(2x)

C. 2e^(x)

D. e^(x)

Correct Answer :

A. 2e^(2x)


Related Questions

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4

What does the definite integral ?(a to b) f(x) dx represent geometrically?

A. The average value of f(x) on [a, b]

B. The area between the curve y = f(x) and the x-axis on [a, b]

C. The derivative of f(x) at x = a

D. The slope of the tangent line to the curve y = f(x) at x = 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

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

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

In three-dimensional space, what are the coordinates of the origin?

A. (0, 0, 0)

B. (1, 1, 1)

C. (0, 0)

D. (1, 1)

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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 line integral ?C F � dr, where C is a curve in the xy-plane and F = ?

A. It depends on the specific curve C.

B. It is always zero.

C. It is equal to the area enclosed by C.

D. It is equal to the circumference of 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

What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?

A. y = x^2 + 1

B. y = x^2

C. y = 2x + 1

D. y = 2x

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4

What is the area of the region enclosed by the polar curve r = 2sin(?)?

A. p square units

B. 4 square units

C. 2 square units

D. 0 square units

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4

What is the dot product of two vectors a and b?

A. |a| × |b| × cos(?)

B. |a| × |b| × sin(?)

C. |a| + |b|

D. |a| - |b|

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4

What is the integral of 1/(x^2 + 1) with respect to x?

A. arctan(x) + C

B. ln(x^2 + 1) + C

C. 2arctan(x) + C

D. (1/2)ln(x^2 + 1) + 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

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

What is the derivative of f(x) = 4x^3 - 2x^2 + 5x - 1 with respect to x?

A. 12x^2 - 4x + 5

B. 12x^2 - 4x - 5

C. 12x^2 - 2x + 5

D. 12x^2 - 2x - 5

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4

The cost C(x) of producing x units of a product is given by C(x) = 3x^2 + 2x + 7. What is the marginal cost when x = 5?

A. 47

B. 37

C. 27

D. 17

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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

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

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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

Which of the following functions is continuous at x = 2?

A. f(x) = 1/x

B. g(x) = x^2 + 3x + 2

C. h(x) = |x - 2|

D. None of the above

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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

If the velocity of an object is given by v(t) = 3t^2, what does ?(1 to 2) v(t) dt represent?

A. The total distance traveled by the object from t = 1 to t = 2

B. The acceleration of the object at t = 1

C. The change in velocity of the object from t = 1 to t = 2

D. The displacement of the object at t = 2

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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

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

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

What does the second derivative of a function represent?

A. The slope of the tangent line

B. The area under the curve

C. The concavity of the curve

D. The average rate of change

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4

The definite integral ?(1 to 3) 2x dx is equal to:

A. 4

B. 8

C. 6

D. 10

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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

Which technique of integration is used to evaluate the integral of a product of two functions, often when integration by parts is required?

A. Trigonometric substitution

B. Integration by substitution

C. Integration by partial fractions

D. Integration by u-substitution

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4

What are the parametric equations for a circle of radius r centered at the origin in polar coordinates?

A. x = rcos(?), y = rsin(?)

B. x = rcos(t), y = rsin(t)

C. x = r?, y = r?

D. x = cos(?), y = sin(?)