${lim}_{x \to a} \frac{\sqrt{x} + \sqrt{a}}{x + a}$

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Solution

${lim}_{x \to a} \frac{\sqrt{x} + \sqrt{a}}{x + a}$

$= \frac{\sqrt{a} + \sqrt{a}}{a + a} = \frac{2 \sqrt{a}}{2 a} = \frac{1}{\sqrt{a}}$

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