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

question 193

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 \(L \neq 0\).

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