# Lim X → 2 X − 2 √ X − √ 2 - Mathematics

$\lim_{x \to 2} \frac{x - 2}{\sqrt{x} - \sqrt{2}}$

#### 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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.4 | Q 14 | Page 28

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