Ok well i did problems like this before but now im having trouble with this one for some reason.(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]f(x) = \frac{1}{\sqrt{x}}[/tex]. Give a [tex]\delta[/tex] - [tex]\epsilon[/tex] proof that [tex]f(x)[/tex] has a limit as [tex]x \rightarrow 4[/tex].

So the defn of a limit is

[tex]\forall \epsilon > 0 \exists \delta > 0[/tex] such that whenever [tex]0 < |x - 4| < \delta[/tex] then [tex]|f(x) - l| < \epsilon[/tex]

Assuming the limit we are trying to prove is [tex]l[/tex].

So i know i somehow have to turn [tex]|f(x) - l| < \epsilon[/tex] into something with [tex]x - 4 < ...[/tex] and that will prove that the limit exists. Am i correct? Am i on the right track? can i assume that [tex]l = \frac{1}{2}[/tex] since [tex]\frac{1}{\sqrt{4}}[/tex]?

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# Delta - epsilon proof

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