lim _ x → 0 √( 2 + x ) √( 2 ) x [ using L ^ ' H . Rule; lim _ x → 0 1 2 √( 2 + x ); = 1 2 √( 2 ) ] ...

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Algebra of Limits

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Question

Solve $lim x \to 0 \frac{\sqrt{2 + x} - \sqrt{2}}{x}$

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Solution

${lim}_{x \to 0} \frac{\sqrt{2 + x} - \sqrt{2}}{x}$
$\begin{matrix} using L^{'} H . Rule {lim}_{x \to 0} \frac{1}{2 \sqrt{2 + x}} = \frac{1}{2 \sqrt{2}} \end{matrix}$

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