10 questions

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1.

The graph of f is shown above, and f is twice differentiable. Which of the following has the largest value?

I. f(0)

II. f′ (0)

III. f″ (0)

2. .

3. .

4.

A slope field for a differential equation is shown above. Which of the following could be the differential equation?

5. Which of the following is a Taylor series for xe^{2x} about x = 0 ?

6. If converges and 0 < a_{k} ≤ b_{k} for all k, which of the following statements must be true?

7. If , then f(x)=

8. A solid has a circular base of radius 1. If every plane cross section perpendicular to the x-axis is a square, then the volume of the solid is

9. If n is a positive integer, then

10. The area enclosed by the parabola y = x - x^{2} and the x-axis is revolved about the x-axis. The volume of the resulting solid is