# 15 multiple choice

1.

Evaluate . (5 points)

 33 42 45 135

2.

Use geometry to evaluate where . (5 points)

3.

Find F ‘(x) for . (5 points)   None of these

4.

Find the antiderivative of . (5 points)   None of these

5.

Evaluate . (5 points)    6.

Use your calculator to evaluate . (5 points)

 0.152 -0.218 0.262 -0.555

7.

R is the 4th quadrant region enclosed by the x-axis and the curve y = x2 – 2kx, where k > 0. Find the value of k so that the area of the region R is 36 square units. (5 points)

 2 3 4 6

8.

The base of a solid is bounded by the curve , the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid. (5 points)

 0.5 3.464 4.5 None of these

9.

Find the average value of f(x) = cos(x) on the interval [0, ]. (5 points)

 1 Ï€ 0

10.

Find the domain for the particular solution to the differential equation , with initial condition y(2) = 2. (5 points)

 x > -2 [-4, 4] All real numbers

11.

The slope field for a differential equation is shown in the figure. Determine the general solution of this equation. (5 points)

 y=Cx2 x=Cy2 y2 – x2 = C2 x2 + y2 = C2

12.

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4 intervals between those given points. (5 points)

x 4 9 11 14 15
f(x) -6 -11 -18 -21 -25
 -12.727 -11.546 -16.273 -13.909

13.

If the graph of f ‘(x) has an x-intercept at x = c, which of the following must be true? (5 points)

 The graph of f has a relative minimum or relative maximum at x = c. The graph of f has an inflection point at x = c. The graph of f has an x-intercept at x = c. None of the above is necessarily true.

14.

Which of the following shows that f(x) grows faster than g(x)? (5 points)   None of these

15.

Find F ‘(x) for . (5 points)

 sin(24) – sin(x12) sin(x7) -sin(x12) -3x2sin(x12)

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