Cho \(\mathop {\lim }\limits_{x \to a} f(x) = L{\rm{  (L}} \in {\rm{R,L}} \ne {\rm{0)}},{\rm{  }}\mathop {\lim }\limits_{x \to a} g(x) =&nbs

A. \(\mathop {\lim }\limits_{x \to a} [f(x).g(x)] = 0\)

B. \(\mathop {\lim }\limits_{x \to a} [f(x).g(x)] =  + \infty \)

C. \(\mathop {\lim }\limits_{x \to a} \frac{{g(x)}}{{f(x)}} =  + \infty \)

D. \(\mathop {\lim }\limits_{x \to a} \frac{{f(x)}}{{g(x)}} = 0\)