Question

limit x->0 [ [(4+x)^(1/2)] -2 ]/x=?

Answer 1

The answer is 1/4

Answer 2

Hint: you multiple both nominator and denominator by \[\sqrt{(4+x)} +2 \]

Answer 3

\[\lim_{x \rightarrow 0}\frac{4+x-4}{x(\sqrt{4+h}+2)}=\lim_{x \rightarrow 0}\frac{1}{\sqrt{4+h}+2}=\frac{1}{4}\]

Answer 4

rationalizing the numerator!.....Got it! :)