# 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 **emphasizes** that we are taking a change in

(The

The difference is only the notation. Personally, I find it clearer to use either

I typically see

The point of **the length of the examination window**. One could easily say

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 (** is** the slope at that point.