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1. If the MacLaurin series for ex 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.
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 = t3 + 2t - 1 and y = t2. 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 3x2 + 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)?