Solve the Problem $x = y ^ { 3 }$ Is Revolved About The

question 170

Essay

Solve the problem.
-The curve $x = y ^ { 3 }$ is revolved about the $x$ -axis. Find a parametrization of the surface of revolution and then find the equation of the tangent plane at the point $( x , y , z ) = ( 8,0,2 )$ .

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Definitions:

Reactance

A psychological reaction that occurs when an individual feels their freedom to choose is being restricted, leading them to resist or do the opposite of what is being imposed.

Dissonance

A psychological conflict resulting from incongruous beliefs and attitudes held simultaneously.

Temporal Discounting

The tendency for people to value immediate rewards more highly than future rewards, often leading to impulsive decisions.

Risk Aversion

The tendency to prefer certainty over uncertainty, characterized by a preference for safe options over risky ones.