=
=
Now, if h approaches 0, what do you have?.
there are two mainstream definitions for the derivative in terms of limits.
Given a function we can find it derivative, via one of the following definitions:
Definition 1:
For a function , it's derivative, , at an arbitrary point is given by:
Defintion 2:
For a function , it's derivative, , at an arbitrary point is given by:
Obviously, galactus employed the first definition. Now the question stands as to whether you can actually evaluate the limit. In the form galactus left it, there was no problem in plugging in h = 0, so that is all that is required to evaluate the limit as h goes to zero. As the definition was at the beginning we could not plug in h = 0 since that would result in the fraction being undefined.