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I just want to get a better grasp of this concept. I don't think you can, for example $F(x) = 1000x$.

If I want to be within $1000$ of $f(x)$, i.e. $\epsilon = 1000$, then $\delta$ would be $250$.

So, $f(249) = 249,000$ - which is not within $1,000$ of $x$, if $x = 1$.

Is this correct?

Thanks!

  • 3
    You are correct that delta will not always be a fourth of epsilon.2012-04-23
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    The $\delta$ you pick depends on (i) the function $f$; (ii) the point $x_0$; and (iii) the $\epsilon$. Note that you want $f(x)$ to be within $\epsilon$ of $f(1)$, not of $1$. For this particular function, $\delta=\epsilon/4$ is not good enough.2012-04-23
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    If this were possible there would be no need for the whole $\delta$ vs. $\epsilon$ business$\ldots\ $.2012-04-23
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    It is a well-known canard that Freshmen believe all functions to be linear. For example, $1/(x+y) = 1/x + 1/y$ is obvious, no?2012-06-01

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