Related Questions
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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 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
If a particle's position at time t is given by r(t) = <3t, t^2, 2t - 1>, what is its velocity vector v(t)?
B. v(t) = <3t, t^2, 2t - 1>
D. v(t) = <2, 2t, 2t - 1>
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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>?
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4
The integral ?(0 to 1) x^3 dx is equal to:
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4
What is the limit of (sin x) / x as x approaches 0?
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4
What is the area of the region enclosed by the polar curve r = 2sin(?)?
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4
What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?
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4
What is the limit of f(x) as x approaches 3 for the function f(x) = 2x + 1?
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4
In parametric equations, what do the variables x and y depend on?
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4
What is the equation of the polar curve r = 2cos(?)?
A. A circle centered at the origin
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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
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4
If f(x) = sin(x), what is f'(x)?
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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 integral of 3x^2 with respect to x?
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4
If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?
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4
What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?
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4
Which of the following limits does not exist?
B. lim (x -> 2) (x^2 - 4)/(x - 2)
C. lim (x -> 1) (x^2 - 1)/(x - 1)
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4
What is the area under the curve y = sin(x) from x = 0 to x = p?
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4
Which of the following functions is continuous at x = 2?
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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?
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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 trigonometric substitution is commonly used to integrate rational functions involving v(a^2 - x^2)?
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4
What is the dot product of two vectors a and b?
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4
What is the derivative of f(x) = 4x^3 - 2x^2 + 5x - 1 with respect to x?
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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
Which of the following is an exact differential equation?
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4
What is the derivative of ln(x) with respect to x?
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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?
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4
What is the integral of vx with respect to x?