Related Questions
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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
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 is the derivative of the vector-valued function r(t) = <2t, t^2, 3t + 1> with respect to t?
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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
The definite integral ?(1 to 3) 2x dx is equal to:
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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 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 distance between the points A(2, -1, 3) and B(4, 3, -2)?
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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
If f(x) = sin(x), what is f'(x)?
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If h(x) = e^(2x), what is h'(x)?
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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 general solution to the differential equation dy/dx = 3x^2?
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4
What is the unit vector in the direction of vector v = <4, -3>?
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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 limit of (sin x) / x as x approaches 0?
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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
What is a vector?
C. A quantity with magnitude and direction
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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?
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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?
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4
Which method is commonly used to solve separable differential equations?
C. Separation of variables
D. Variation of parameters
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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
What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?
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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
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 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 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
What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?