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the line x=1)

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(1)

1 x y

The line L in the figure above is moving from left to right at the rate of 3/2 units per second. What is the rate at which the area of the region under the curve

that lies to the right of the y‐axis and is being swept by L is changing?

L

(2)

1 x y

c

Ac Bc

Let Ac (resp. Bc) denote the area of the region under the curve

between the line x=c and the y‐axis (resp. the line x=1). Show that there exists exactly one c such that Ac = Bc.

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