Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$

question 5

Multiple Choice

Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$ for $f ( x ) = 4 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 5 } } { 3 x ^ { 2 } }$ .

• A) \(\frac { 20 \sqrt { 30 } } { 3 }\)
• B) limit does not exist
• C) \(\frac { \sqrt { 6 } } { 3 } + 500\)
• D) \(\frac { \sqrt { 6 } } { 3 } - 500\)
• E) \(\frac { \sqrt { 30 } } { 75 } - 500\)

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Definitions:

Marginal Cost

The additional cost incurred in the production of one more unit of a good or service.

Total Revenue

The total amount of money a company receives from its business activities, calculated by multiplying the price of goods or services by the quantity sold.

Total Cost

The aggregate amount of expenses that a company or individual incurs to produce or acquire goods or services.

Short-run Supply Curve

A graphical representation showing the relationship between the price of a good or service and the quantity supplied over a short period, during which at least one input is fixed.