\[y\]exists, if [RPET 1995]

• A.                 \[{{x}_{n+1}}=\sqrt{2+{{x}_{n}}},\ n\ge 1,\ \] and \[\underset{x\to a}{\mathop{\lim }}\,g(x)\] exist
• B.                 \[\underset{x\to a}{\mathop{\lim }}\,f{{(x)}^{g(x)}}\] exists
• C.                 \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}\] exists
• D.                 \[\underset{x\to a}{\mathop{\lim }}\,f(x)g\left( \frac{1}{x} \right)\]exists