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1. As the tides change, the water level in a bay varies sinusoidally. At high tide todayat 8 A.M., the water level was 15 feet; at low tide, 6 hours later at 2 P.M., it was 3 feet. How fast, in feet per hour, was the water level dropping at noontoday?
2. Let sin πx. Then f (3) =
3. is equal to
4. Given f (x) = log10x and log10(102) 2.0086, which is closest to f ′(100)?
5. If G(2) = 5 and then an estimate of G(2.2) using a tangent-line approximation is
6. The area bounded by the parabola y = x2 and the lines y = 1 and y = 9 equals
7. The first-quadrant region bounded by y = 0, x = q (0 < q < 1), and x = 1 is rotated about the x-axis. The volume obtained as q →0+ equals
8. A curve is given parametrically by the equations
x = 3 - 2sint and y = 2cos t - 1.
The length of the arc from t = 0 to t = π is
9. Suppose the graph of f is both increasing and concave up on a ≤ x ≤ b. Then, using the same number of subdivisions, and with L, R, M, and T denoting, respectively, left, right, midpoint, and trapezoid sums, it follows that