Is there a difference between #lim_(h->0)(f(x+h)-f(x))/h# and #lim_(deltax->0)(f(x+deltax)-f(x))/(deltax)#?
3 Answers
Yes, there is a difference since the first limit is defined at
I hope that this was helpful.
It is only a different notation.
Explanation:
I've never seen this with a lower case
We treat
You might say that the
(The
The difference is only the notation. Personally, I find it clearer to use either
I typically see
The point of
The whole idea of this limit derivative definition is to say that when you zoom into a graph (with your calculator, for instance), the more you zoom in, the more linear the graph looks (and the smaller this
and you modify it to use this new miniscule window width,
where
So really, this is saying that since this slope exactly lines up with the graph on a really close zoom (