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1. If the MacLaurin series for e^{x} is , what is a power series expansion for ?

2. The rate of growth of algae, A, in a pond with respect to time, t, is directly proportional to one half the amount of algae in the pond. Which differential equation describes this relationship?

3. If f(x) dx = 100 and f(x) dx = 75, find f(x) dx.

4.

Which of the following is the differential equation of the slope field above?

5. The length of a curve from x = 2 to x = 3 is given by . If the curve contains the point (2, 10), which of the following could be the curve?

6. If the line tangent to the graph of the function f at the point (8, 2) passes through the point (2, 5), then f′(8) =

7. A curve is defined by the parametric equations x = t^{3} + 2t - 1 and y = t^{2}. Which of the following is an equation of the line tangent to the graph at (11, 4)?

8. The graph of the function f is shown below

If g(x) = dt, what is g′(2)?

9. If the graph of y = f(x) has slope 3x^{2} + 5 at each point (x,y) on the curve and it passes through (2, 18), which of the following is the equation of f(x)?