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1. Find the area inside one loop of the curve r = sin 2θ.

2. The average value of sec^{2} x on the interval is

3. Find the length of the arc of the curve defined by x = t^{2} and y = , from t = 0 to t = 2.

4. The function f is given by f(x) = x^{4} + 4x^{3}. On which of the following intervals is f decreasing?

5. Which of the following series converge(s)?

I.

II.

III.

6. Given the differential equation , where z(0) = 50, what is z(t)?

7.

The slope field shown above corresponds to which of the following differential equations?

8. The value of c that satisfies the Mean Value Theorem for derivatives on the interval [0, 5] for the function f(x) = x^{3} – 6x is

9.

The graph of f is shown in the figure above. If g(x) = f(t) dt, for what positive value of x does g(x) have a minimum?