The area of a circle diffuses out a constant rate of 0.0000197 m^2/s. Create a formula to find the instantaneous velocity of the radius. Calculus the instantaneous velocity of the radius at 0 and 1 seconds. The circle begins as a single point.
xyzzy
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
ted s
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
alex
hint:
1/
A = pi r^2
find dr/dt