Calculus SE4

lim(x->b) of b-x/sqrt(x)-sqrt(b)

A. -2sqrt(b)

If f(x)=3xlnx, then f'(x)=

A. 3+ln(x^3)

The volume of an expanding sphere is increasing at a rate of 12 cubic feet per second. When the volume of the sphere is 36π cubic feet, how fast, in square feet per second, is the surface area increasing?

A. 8

If y=1-x/x-1, then dy/dx=

B. 0

Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y=x^2-2kx, where k>0. If the area of the region R is 36, then the value of k is

B. 3

Integral from 2 to 4 [d/dt(3t^2+2t-1)]dt=

B. 40

If at each point (x,y) on a certain curve is 2y/x, then the curve is a(n)

B. Parabola

Which of the following functions sketched below is increasing at a decreasing rate?

C.

For what values of x does 4x^8-8x^3+18 have a relative minimum?

C. 1 only

Let f(x) be a continuous and differentiable function. The table below gives the value of f(x) and f'(x), the derivative of f(x), at several values. If g(x)=1/f(x), what is the vlaue of g'(2)?

C. 1/16

The position of a particle on the x-axis at time t, t>0 is lnt. The average velocity of the particle for 1<t<e is

C. 1/e-1

integral from -3 to 3 of abs(x+2)dx=

C. 13

If the integral from 1 to 7 of lnxdx is approximated by 3 circumscribed rectangles of equal width on the x-axis, then the approximation is

C. 2(ln3+ln5+ln7)

Which definite integral represents the volume of a sphere with radius 2?

C. 2π* integral from 0 to 2 of (4-x^2)dx

What is the area of the shaded region in the figure to the right?

C. 4

Which of the following are the equations of all horizontal and vertical asymptotes for the curve y=x/x(x^2-4)?

C. y=0 and x=-2 and 2

If the substitution u=25-x^2 is made, the integral from o to 3 of (xsqrt(25-x^2))dx =

D. 1/2*integral from 16 to 25 of sqrt(u)du

integral of (3x+5)^2dx=

D. 1/9(3x+5)^3

The minimum value of f(x)=e^x-2x is

D. 2(1-ln2)

lim(h->0) of tan2(x+h)-tan(2x)/h is

D. 2sec^2(2x)

The velocity of a particle moving along the x-axis is given by a third-degree polynomial P(t). The roots of P(t) are all in the open interval 0<t<a. Which of the following statements must be true?

D. I and II only

Which of the following statements is true?

D. I and III only

The graph of y=f(x) on the closed interval [-3,7] is shown in the figure to the right. If f is continuous on [-3,7] and differentiable on (-3,7), then there exists a c, -3<c<7, such that

D. f'(c)=-1/5

The graph of a function f whose domain is the closed interval [1,7] is shown to the right. Which of the following statements about f(x) is true?

D. f(x) is continuous at x=3

If y=arcsin(3x/4), then dy/dx =

E. 3/sqrt(16-9x^2)

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then its volume is

E. 36sqrt(3)

At which of the three points on the graph y=f(x) in the figure shown is f'(x)<f"(x)?

E. A and C

If f(x) = 3 + abs(x-2), then f'(2) is

E. nonexistent