Find $$\lim _ { x \rightarrow 3 } [ g ( x ) - f ( x ) ]$$

Multiple Choice

Find
$$\lim _ { x \rightarrow 3 } [ g ( x ) - f ( x ) ]$$
for $f ( x ) = 3 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 2 } } { 6 x ^ { 2 } }$ .

A) $\frac { \sqrt { 11 } } { 54 } - 81$
B) $\frac { \sqrt { 3 } } { 6 } - 81$
C) $\frac { 3 \sqrt { 11 } } { 2 }$
D) $\frac { \sqrt { 3 } } { 6 } + 81$
E) limit does not exist