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If $\lim _{\mathrm{x} \rightarrow \mathrm{a}}\left[\frac{\mathrm{f}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\right]$ exists, then which one of the following correct $?$

MathematicsLimitsNDANDA 2006 (Phase 2)

Options:

A Both $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ must exist
B $\lim _{x \rightarrow a} f(x)$ need not exist but $\lim _{x \rightarrow a} g(x)$ must exist
C Both $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ need not exist
D $\lim _{x \rightarrow a} f(x)$ must exist but $\lim _{x \rightarrow a} g(x)$ need not exist

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