Find the Equation for the Plane Tangent to the Parametrized

question 69

Short Answer

Find the equation for the plane tangent to the parametrized surface S at the point P.
- $$\text { S is the cylinder } r ( \theta , z ) = 8 \cos \theta \mathbf { i } + 8 \sin \theta \mathbf { j } + \mathrm { zk } ; \mathrm { P } \text { is the point corresponding to } ( \theta , \mathrm { z } ) = \left( \frac { \pi } { 2 } , 3 \right) \text {. }$$

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Definitions:

Retina

A layer at the back of the eyeball containing cells that are sensitive to light and trigger nerve impulses that pass via the optic nerve to the brain, where a visual image is formed.

Sensation

The process by which sensory receptors and the nervous system receive stimuli from the environment, such as touch, taste, smell, sound, and sight.

Perception

The process by which sensory information is organized, interpreted, and consciously experienced.

20,000 Hz

The frequency of soundwaves that typically represents the upper limit of human hearing.