Provide an Appropriate Response $\sqrt [ n ] { n ! } \approx \frac { n } { e }$

question 197

Multiple Choice

Provide an appropriate response.
-It can be shown that $\sqrt [ n ] { n ! } \approx \frac { n } { e }$ for large values of $n$ . Find the smallest value of $N$ such that $\frac { \sqrt [ n ] { n ! } } { \frac { n } { e } } - 1 < 10 ^ { - 1 }$ for all $\mathrm { n } > \mathrm { N }$ .

• A) 29
• B) 33
• C) 27
• D) 22

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Definitions:

Motor Neuron

A type of nerve cell that transmits signals from the brain and spinal cord to muscles, stimulating them to contract.

Effector Organ

An organ or tissue that reacts to a stimulus from the nervous system to produce a specific response.

Cauda Equina

The cauda equina is a bundle of spinal nerves and spinal nerve rootlets below the end of the spinal cord, resembling a horse's tail, which distributes nerve roots to the lower limbs and pelvic organs.

Filium Terminale

The filium terminale is a slender filament of connective tissue that extends from the conus medullaris at the lower end of the spinal cord to the coccyx, anchoring the spinal cord in place.