Question

how to solve the above sum

Answer 1

$lim _{x - > 0} \: \: \: \frac{ \sqrt{x + 2} - \sqrt{2} }{x} \\ put \: x \: = 0 \\ we \: get \: a \: \: \: \frac{0}{0} \: form \:...hence \: we \: need \: to \: simplify \: it \: \\ \\ multiply \: both \: numerator \: and \: \: Denominator \: by \: ( \sqrt{x + 2} + \sqrt{2} ) \\ = > lim _{x - > 0} \: \: \: \frac{ (\sqrt{x + 2} - \sqrt{2} \times) \times ( \sqrt{x + 2} + \sqrt{2})}{x \times ( \sqrt{x + 2} + \sqrt{2}) \: } \\ = lim _{x - > 0} \: \: \: \frac{1}{ \sqrt{x + 2} + \sqrt{2} } \\ put \: x \: = 0 \: \\ = > lim _{x - > 0} \: \: \: \frac{ \sqrt{x + 2} - \sqrt{2} }{x} \: = \frac{1}{2 \sqrt{2} }$