Show That the Function Has Exactly One Zero in the Given

question 29

Essay

Show that the function has exactly one zero in the given interval.
- $r ( \theta ) = 4 \cot \theta + \frac { 1 } { \theta ^ { 2 } } + 6 , ( 0 , \pi )$

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Definitions:

Perceptual Constancy

The phenomenon that allows us to perceive objects as maintaining stable properties, such as size, shape, and brightness, despite differences in distance, viewing angle, and lighting.

Objects

In psychology, objects can refer to physical items in the external world that can be perceived by the senses, often studied in the context of how humans interact with and attribute meaning to them.

Vestibular Senses

Vestibular senses are related to balance and spatial orientation, arising from the vestibular system in the inner ear, helping to maintain equilibrium and coordinate movements.

Movement

The process of changing the physical location or position of something, or a group's effort to advance their interests or beliefs.