limit strategy/rate of change

Question

A raindrop falls to the ground from the height 's' meters. After 't' seconds the raindrop is 's' meters above the ground where s(t)= 120-2t^2

 

Find rate of change in height 's' when t= 4 seconds

find answer using limit strategy 

Answer 1

First of all this is a derivative problem where the derivative is -2t and at t = 4 the velocity is -4.

 

The limit process to get there works like this:

s(4+h) = 120 - 2(4 + h)² = 120 -16 -8h - h²

s(4) = 120 -2(4*4) = 120 -16

s(4+h) - s(4) = -8h - h²

[s(4+h) - s(4)]/h = -8 - h

 

The limit of the left side as h --> 0 is the instantaneous velocity at t=4 and it is the limit of the right side which is -8.