Cho \(\mathop {\lim }\limits_{x \to {x_0}} f\left( x \right) = L \ne 0\). Trong các mệnh đề sau,mệnh đề nào sai?

A. \(\mathop {\lim }\limits_{x \to {x_0}} \sqrt {f\left( x \right)}  = \sqrt L \)

B. \(\mathop {\lim }\limits_{x \to {x_0}} \sqrt[3]{{f\left( x \right)}} = \sqrt[3]{L}\)

C. \(\mathop {\lim }\limits_{x \to {x_0}} {\left[ {f\left( x \right)} \right]^2} = {L^2}\)

D. \(\mathop {\lim }\limits_{x \to {x_0}} \left( {\frac{1}{{f\left( x \right)}}} \right) = \frac{1}{L}\)