Find the Formula and Limit as Requested $\mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } + 3$

question 22

Multiple Choice

Find the formula and limit as requested.
-For the function $\mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } + 3$ , find a formula for the upper sum obtained by dividing the interval [0,3] into $n$ equal subintervals. Then take the limit as $n \rightarrow \infty$ to calculate the area under the curve over $[ 0,3 ]$ .

• A) \(9 + \frac { 33 n ^ { 2 } + 37 n } { 2 n ^ { 2 } } ;\) Area \(= \frac { 51 } { 2 }\)
• B) \(9 + \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= \frac { 54 } { 5 }\)
• C) \(9 + \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= 27\)
• D) \(9 - \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= - 9\)

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Definitions:

Supply Curve

A graph that illustrates the relationship between the price of a good or service and the amount of it that producers are willing to supply at each price level.

Orange Market

A specific sector for trading or selling oranges, which can serve as a proxy for understanding supply and demand dynamics in agricultural markets.

Law Of Supply

A principle that states there is a direct relationship between the price of a good and the quantity of it producers are willing to supply. As the price of a good increases, producers will wish to supply more of it. As the price decreases, producers will wish to supply less.

Producers

Individuals or businesses that create goods or provide services.