If \[\underset{x\to a}{\mathop{\lim }}\,\left[ \frac{f(x)}{g(x)} \right]\]exist, then which one of the following correct?

• A. Both \[\underset{x\to a}{\mathop{\lim }}\,f(x)\] and \[\underset{x\to a}{\mathop{\lim }}\,g(x)\] must exist
• B. \[\underset{x\to a}{\mathop{\lim }}\,f(x)\] need not exist but \[\underset{x\to a}{\mathop{\lim }}\,g(x)\] must exist
• C. Both \[\underset{x\to a}{\mathop{\lim }}\,f(x)\] and \[\underset{x\to a}{\mathop{\lim }}\,g(x)\] need not exist
• D. None of these