Unformatted text preview: r ( t ? ). The only rate that we are given is for the rate of change of area, so one idea would be to relate r ( t ) to A ( t ) in hopes of being able to learn more about r ( t ) from A ( t ). To this end, we use the area formula A ( t ) = πr 2 ( t ) , valid for t > 0, and diﬀerentiate this relationship with respect to t , A ( t ) = 2 πr ( t ) r ( t ) . It follows that for t = t ? , r ( t ? ) = A ( t ? ) 2 πr ( t ? ) = 2 2 π · 3 = 1 3 π mm/sec . Substituting this value back into (1), we determine C ( t ? ) = 2 π 1 3 π = 2 3 mm/sec ....
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 Fall '10
 KIHYUNHYUN
 Calculus, Rate Of Change

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