Definition of the Derivative using delta and epsilon

[jfy4]

Hi,

I have a question about the formulation of the derivative. The definition is

[tex]f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}[/itex]<br /> <br /> Lets say this limit exists. Can I write the limit in the typical $\epsilon-\delta$ method as such<br /> <br /> <i>Given the limit exists, then for all $\epsilon>0$ there exists a $\delta>0$ such that $|x-x_0|<\delta\implies$</i><br /> $$\left|\frac{f(x)-f(x_0)}{x-x_0}-f'(x_0)\right|<\epsilon$$<br /> <br /> ?[/tex]

 

[Rasalhague]

Yes, the word "limit" and the "lim" notation mean just the same here as they usually do.

 

[jfy4]

Yes, the word "limit" and the "lim" notation mean just the same here as they usually do.

Thanks