Calculus Problem: Expanding Circle?

A = pi r^2

dA/dt = 2pi r dr/dt = k

but that isn't all that usefull because we don't know what r is at time t... we know it is 0 at t=0...otherwise no help

how about...

A(t) = k t

A = pi r^2

r(t) = (k/pi t)^1/2

dr/dt = 1/2 (k/pi t)^-1/2 k/pi

=1/2 (pi/k t)^-1/2

undefined at t = 0

1/2 (k/pi)^1/2 at t = 1

A = π r² ..given dA/dt for all t ( call this C );..but dA/dt = 2 π r dr/dt ---> C / 2 = r dr/dt --->

C/2π t + K = r² / 2..r(0) = 0 { given } so K = 0---> r = √ (C t / π )---> r(1) = √ (C / π )....

thus dr/dt when t = 0 is { as it should be } infinite while when t = 1 is √ ( C π ) / 2

hint:

1/

A = pi r^2

find dr/dt