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## Main Question or Discussion Point

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]

Lets say this limit exists. Can I write the limit in the typical [itex]\epsilon-\delta[/itex] method as such

[tex]\left|\frac{f(x)-f(x_0)}{x-x_0}-f'(x_0)\right|<\epsilon[/tex]

?

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]

Lets say this limit exists. Can I write the limit in the typical [itex]\epsilon-\delta[/itex] method as such

*Given the limit exists, then for all [itex]\epsilon>0[/itex] there exists a [itex]\delta>0[/itex] such that [itex]|x-x_0|<\delta\implies[/itex]*[tex]\left|\frac{f(x)-f(x_0)}{x-x_0}-f'(x_0)\right|<\epsilon[/tex]

?