Question

${lim}_{x\to 0}\frac{(1+x{)}^{1/4}-(1-x{)}^{1/4}}{x}$ is equal to :

Answer 1

$\underset{x\to 0}{lim}\frac{(1+x{)}^{1/4}-(1-x{)}^{1/4}}{x}=$indeterminate form

Applying L-Hospital rule

$\underset{x\to 0}{lim}\frac{\frac{1}{4}(1+x{)}^{-3/4}+\frac{1}{4}(1-x{)}^{-3/4}}{1}=\frac{1}{2}$