Trying to find the limit....?

Question

I am trying to find the limit of the following, but am not able to finish...

lim (h->0) of [(2+h)^3 - 8] / [h]

This is what I have thus far:

lim (h->0) of [(2+h)^3 - 8] / [h] =

[6h^2 + 12h + h^3] / [h] =

6h + 12 + h^2 =

lim (h->0) = ???

Since 12 is the constant, would it be 12?

Thanks....

Answer 1

You are perfectly right.
lim(h goes to 0) (6h+12+h^2). Here you simply put h=0
So the answer is 12. OK

Answer 2

your math is off. taking the limit becomes undefined of N/0, so you must perform L'Hopital's rule, taking the derivative of the numerator and then the denominator seperately.

that gives you - (3h^2 + 12h + 12)/1

but you do get 12 when you take the limit.

Answer 3

I believe so.