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:

Procedural Memory

A type of long-term memory for performing specific tasks, not requiring conscious thought for actions or skills learned through repetition.

Explicit Memory

A type of long-term memory involving the conscious recollection of factual information, previous experiences, and concepts.

Korsakoff's Syndrome

A chronic memory disorder often caused by severe deficiency of thiamine (vitamin B1), usually due to long-term alcohol abuse.

Vitamin B-1

Thiamine, known as Vitamin B-1, is essential for glucose metabolism and plays a critical role in nerve, muscle, and heart function.