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
What is the derivative of the constant function f(x) = 7?
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4
If a point has polar coordinates (r, ?), what are its Cartesian coordinates?
A. x = rcos(?), y = rsin(?)
C. x = cos(?), y = sin(?)
D. x = rsin(?), y = rcos(?)
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4
What is the general solution to the differential equation dy/dx = 3x^2?
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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)?
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4
What is the unit vector in the direction of vector v = <4, -3>?
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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
If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?
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Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?
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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
The definite integral ?(1 to 3) 2x dx is equal to:
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4
Which of the following functions is continuous at x = 2?
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What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?
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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.
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 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
What is a vector?
C. A quantity with magnitude and direction
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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 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)
D. x = cos(?), y = sin(?)
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4
What is the limit of (sin x) / x as x approaches 0?
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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
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
Which of the following is an exact differential equation?
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4
What is the dot product of two vectors a and b?
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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
In parametric equations, what do the variables x and y depend on?
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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
The area between the curve y = x^2 and the x-axis from x = 0 to x = 2 is equal to:
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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 integral of 3x^2 with respect to x?
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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