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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

Correct Answer :

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


Related Questions

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4

Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?

A. Separable

B. Linear

C. Exact

D. Homogeneous

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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 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 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

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 derivative of ln(x) with respect to x?

A. 1/x

B. 1

C. x

D. 0

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4

Which method is commonly used to solve separable differential equations?

A. Laplace transforms

B. Substitution

C. Separation of variables

D. Variation of parameters

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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

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

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

A. 2e^(2x)

B. e^(2x)

C. 2e^(x)

D. e^(x)

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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

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 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

If a point has polar coordinates (r, ?), what are its Cartesian coordinates?

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

B. x = r?, y = r?

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

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

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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

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 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 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 unit vector in the direction of vector v = <4, -3>?

A. <1, 1>

B. <2, -1.5>

C. <4/5, -3/5>

D. <0, 0>

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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(?)

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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 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

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

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 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

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

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 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

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