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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

Correct Answer :

B. 6


Related Questions

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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

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 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 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 limit of (sin x) / x as x approaches 0?

A. 1

B. 0

C. -1

D. Undefined

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

A. 1/x

B. 1

C. x

D. 0

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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 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 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

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

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

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

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

A. 4

B. 8

C. 6

D. 10

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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 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

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

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

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

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

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 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 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

A ball is thrown into the air, and its height (in meters) above the ground at time t (in seconds) is given by h(t) = 4.9t^2 + 15t + 2. What is its initial velocity?

A. 4.9 m/s

B. 15 m/s

C. 2 m/s

D. 0 m/s

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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 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 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 integral of e^(3x) with respect to x?

A. (1/3)e^(3x) + C

B. 3e^(x) + C

C. (1/3)e^(x) + C

D. e^(3x) + C

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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 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