A Manufacturer of Light Bulbs Wants to Produce Bulbs That $F ( t )$

question 135

Short Answer

A manufacturer of light bulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let $F ( t )$ be the fraction of the company's bulbs that burn out before $t$ hours. $F ( t )$ lies between 0 and 1 .
Let $r ( t ) = F ^ { \prime } ( t )$ . What is the value of $\int _ { 0 } ^ { \infty } r ( t ) d t$ ?

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Definitions:

Insula

A region of the brain located deep within the lateral sulcus, involved in functions related to emotion and the regulation of the body's homeostasis.

Filiform Papillae

Filiform papillae are small, thread-like structures on the tongue's surface that do not contain taste buds but are important for the texture and sensation of food.

Ethmoid

A spongy, cuboid-shaped bone located at the roof of the nasal cavity and part of the floor of the anterior cranial fossa; crucial for olfaction and nasal support.

Olfactory Perception

The sense of smell, a complex process involving the detection and identification of volatile substances by the olfactory system.