$\mathop {\lim }\limits_{x \to a} f(x) \cdot g(x)$ exists,if
- A$\mathop {\lim }\limits_{x \to a} f(x)$ and $\mathop {\lim }\limits_{x \to a} g(x)$ exist
- B$\mathop {\lim }\limits_{x \to a} f(x)^{g(x)}$ exists
- C$\mathop {\lim }\limits_{x \to a} \frac{f(x)}{g(x)}$ exists
- D$\mathop {\lim }\limits_{x \to a} f(x)g\left( \frac{1}{x} \right)$ exists
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