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Question
\[\lim_{x \to 2} \frac{x - 2}{\sqrt{x} - \sqrt{2}}\]
Solution
\[\lim_{x \to 2} \left[ \frac{x - 2}{\sqrt{x} - \sqrt{2}} \right]\] It is of the form \[\frac{0}{0}\]
⇒ \[\lim_{x \to 2} \left[ \frac{\left( \sqrt{x} \right)^2 - \left( \sqrt{2} \right)^2}{x - \sqrt{2}} \right]\]
= \[\lim_{x \to 2} \left[ \frac{\left( \sqrt{x} - \sqrt{2} \right)\left( \sqrt{x} + \sqrt{2} \right)}{\left( x - \sqrt{2} \right)} \right]\]
= \[\sqrt{2} + \sqrt{2}\]
= \[2\sqrt{2}\]
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