derivatives and limits

[rn23]

For my calculus class i have to write a paper on derivatives. One of the things that i have to have in it is how derivatives are connected to limits. I have been researching it but i just cannot exactly understand what there realtionship is. Could you please help?

 

[galactus]

All you have to do is google 'definition of a derivative' and you will find something. Also, do you have a calc book?.
That should certainly deal with it, around chapter 2.

Here's one of the main things you're looking for:

\(\displaystyle f'(x)=\lim_{h\to{0}}\frac{f(x+h)-f(x)}{h}\)

A good start may be to show the slope of a line with equation y=mx+b is m for all x.

 

[pka]

Well, a derivative is a limit.
At a point in question on a graph, the derivative is the limiting value of the slopes of all secants of the graph determined by the given point and any other point near the given point.

 

[stapel]

For my calculus class i have to write a paper on derivatives. One of the things that i have to have in it is how derivatives are connected to limits. I have been researching it but i just cannot exactly understand what there realtionship is.

So you studied the chapter in your book on limits, and then you studied the next chapter on the definition of the derivative, which was given as being a limit. And yet you are not aware of any relationship between limits and derivatives...? :shock:

Eliz.