Calculus 1 - Limits

Question

Let v = 50√T. Estimate the instantaneous rate of change of v with respect to T when T = 300.

Answer 1

V = 50 * T^ (1/2)

dV/dT = 25 * t^ ( -1/2)

= 25/ sqrt(t)

At t=3000, the instantaneous rate of change is:

25/ sqrt(3000)

= 25/ sqrt( 3 *10 * 10 * 10)

= 25 / 10 * sqrt(30)

= 25 * sqrt(30) / 300

= sqrt(30) / 12

= 0.456435464587638....