Question

lim x=0
$\sqrt{2 - x} - \sqrt{2} \div x$
​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr0} \frac{ \sqrt{2 - x} - \sqrt{2} }{x}$

$= \lim_{x \rarr0} \frac{( \sqrt{2 - x} - \sqrt{2} )( \sqrt{2 - x} + \sqrt{2} )}{x( \sqrt{2 - x} + \sqrt{2} )}$

$= \lim_{x \rarr0} \frac{2 - x - 2}{x( \sqrt{2 - x} + \sqrt{2}) }$

$= \lim_{x \rarr0} \frac{ - x}{x( \sqrt{2 - x} + \sqrt{2} ) }$

$= \lim_{x \rarr0} \frac{ - 1}{ \sqrt{2 - x} + \sqrt{2} }$

$= \frac{ - 1}{2 \sqrt{2} }$