Consider the following statements: 1. If _ x arrow a f(x) and _ x...

Consider the following statements: 1. If $\lim _{\mathrm{x} \rightarrow \mathrm{a}} f(\mathrm{x})$ and $\lim _{\mathrm{x} \rightarrow \mathrm{a}} \mathrm{g}(\mathrm{x})$ both exist, then $\lim _{\mathrm{x} \rightarrow \mathrm{a}}\{f(\mathrm{x})\mathrm{g}(\mathrm{x})\}$ exists. 2. If $\lim _{x \rightarrow a}\{f(x) g(x)\}$ exists, then both $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ must exist. Which of the above statements is correct?