Question

Evaluate the limit

(6+h)^3-216/h

I think you would have expand the numerator

(6+h)^3 = but how would you do it?

216+108h+h^3? It's not coming out right...

Answer 1

(6+h)^3
= 216 + 3(36h) + 3(6h^2) + h^3
= 216 + 108h + 18h^2 + h^3

so Limit ( (6+h)^3-216 )/h , as h ---> 0
= lim ( 216 + 108h + 18h^2 + h^3 - 216)/h
= lim (108h + 18h^2 + h^3)/h , as h --> 0
= lim 108 + 18h + h^2 , as h --> 0
= 108

check using Calculus as such ...
we were finding dy/dx of
y = x^3, when x = 6
dy/dx = 3x^2
= 3(6^2) = 108