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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Definitions:

Economies of Scale

Cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output generally decreasing with increasing scale as fixed costs are spread out over more units of output.

Diseconomies of Scale

The phenomenon where production costs per unit increase as a firm or production process scales up, contrary to economies of scale where costs decrease.

Boeing

An American multinational corporation that designs, manufactures, and sells airplanes, rotorcraft, rockets, satellites, telecommunications equipment, and missiles worldwide.

Law of Diminishing Returns

An economic principle stating that adding more of one factor of production, while holding others constant, will at some point yield lower per-unit returns.