Let A be the area if the region in the first quadrant under the graph of

y = cos(x) and above the line y = k for

0 < k < 1.

a. Determine A in terms of k.

b. Determine the value of A when k = 1/2

c. If the line y = k is moving upward at a rate of 1/pi units per minute, at what rate is the area A changing when k = 1/2?

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