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Question
\[\lim_{x \to a} \frac{x - a}{\sqrt{x} - \sqrt{a}}\]
Solution
\[\lim_{x \to a} \left[ \frac{x - a}{\sqrt{x} - \sqrt{a}} \right]\]
= \[\lim_{x \to a} \left[ \frac{\left( \sqrt{x} \right)^2 - a^2}{\sqrt{x} - \sqrt{a}} \right]\]
= \[\lim_{x \to a} \left[ \frac{\left( \sqrt{x} - \sqrt{a} \right) \left( \sqrt{x} + \sqrt{a} \right)}{\left( \sqrt{x} - \sqrt{a} \right)} \right]\]
= \[\sqrt{a} + \sqrt{a}\]
= \[2\sqrt{a}\]
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