Definition of the Derivative using delta and epsilon

  • Thread starter jfy4
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  • #1
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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

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]

?
 

Answers and Replies

  • #2
1,384
2
Yes, the word "limit" and the "lim" notation mean just the same here as they usually do.
 
  • #3
649
3
Yes, the word "limit" and the "lim" notation mean just the same here as they usually do.
Thanks
 

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