If the Infinite Curve $y = e ^ { - x } , x \geq 0$

question 103

Multiple Choice

If the infinite curve $y = e ^ { - x } , x \geq 0$ , is rotated about the $x$ -axis, find the area of the resulting surface. Select the correct answer.

• A) \(\pi [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• B) \(\frac { \pi } { 6 } [ \sqrt { 3 } + \ln ( 1 + \sqrt { 3 } ) ]\)
• C) \(\frac { \pi } { 3 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• D) \(\frac { \pi } { 4 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• E) \(\frac { \pi } { 6 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)

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Definitions:

Demand Schedule

A table that shows the quantity of a good or service that consumers are willing to buy at each price point.

Marginal Cost

The incremental expense incurred from the production of an extra unit of a good or service.

Maximum Profit

The highest possible financial gain achievable by a firm from its operations, over a certain period of time.

Demand Schedule

A chart displaying the amount of a product or service that buyers are prepared and capable of buying at different price levels.