Use a CAS to Plot the Function near the Point $\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }$

question 24

Multiple Choice

Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
-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 \(L \neq 0\).
• C) 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 \(f ( a ) \neq 0\).
• D) \(\lim _ { x \rightarrow a } \frac { g ( x ) } { f ( x ) } = \frac { g ( a ) } { f ( a ) }\), provided that \(f ( a ) \neq 0\).

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Definitions:

Work In Process Inventory

Refers to the inventory that has begun the manufacturing process but is not yet completed.

Processing Department

A division within a manufacturing facility where a specific operational task or series of tasks is performed to convert raw material into finished goods or semi-finished goods.

Job Order Cost Cards

Documents used to record and track the materials, labor, and overhead costs assigned to individual jobs or batches in production.

Perpetual Inventory Accounts

An inventory tracking system where updates are made continuously as transactions occur, providing a real-time view of inventory levels.