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Question
\[\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}\]
Solution
\[\lim_{x \to 4} \left[ \frac{2 - \sqrt{x}}{4 - x} \right]\]
= \[\lim_{x \to 4} \left[ \frac{2 - \sqrt{x}}{2 - \left( \sqrt{x} \right)^2} \right]\]
= \[\lim_{x \to 4} \left[ \frac{\left( 2 - \sqrt{x} \right)}{\left( 2 - \sqrt{x} \right)\left( 2 + \sqrt{x} \right)} \right]\]
= \[\frac{1}{2 + \sqrt{4}}\]
= \[\frac{1}{2 + 2}\]
= \[\frac{1}{4}\]
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