Provide an Appropriate Response $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }$

Multiple Choice

Provide an appropriate response.
-Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" and include a statement of any restrictions on the principle.

A) $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }$ .
B) If $\lim _ { x \rightarrow a } g ( x ) = M$ and $\lim _ { x \rightarrow a } f ( x ) = L$ , then $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { \lim _ { x \rightarrow a } g ( x ) } { \lim _ { x \rightarrow a } f ( x ) } = \frac { M } { L }$ , provided that $f ( a ) \neq 0$ .
C) $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }$ , provided that $f ( a ) \neq 0$ .
D) If $\lim _ { x \rightarrow a } g ( x ) = M$ and $\lim _ { x \rightarrow a } f ( x ) = L$ , then $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { \lim _ { x \rightarrow a } g ( x ) } { \lim _ { x \rightarrow a } f ( x ) } = \frac { M } { L }$ , provided that $L \neq 0$ .