Answer by bjorn93 for Use the $\epsilon$ - $\delta$ definition to show that...
First of all, you don't have to prove it this way. You might try to directly work with $\left|\frac{1}{2}\left(\frac{2}{x}+x\right)-\sqrt{2}\right|$, as shown here in the first question you posted...
View ArticleAnswer by Alexey Burdin for Use the $\epsilon$ - $\delta$ definition to show...
$|\frac{2}{x}-\sqrt2| < \epsilon\Leftrightarrow-\epsilon<\frac{2}{x}-\sqrt2 < \epsilon\Leftrightarrow-\epsilon+\sqrt2<\frac{2}{x} <...
View ArticleUse the $\epsilon$ - $\delta$ definition to show that $\lim_{x\to \sqrt2}...
Use the epsilon-delta definition to show that $\lim_{x\to \sqrt2} \frac{1}{2}\left(\frac{2}{x}+x\right) = \sqrt2$.I have been shown the following approach to solve this:Let first $\epsilon >...
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