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:

Emaciation

A state of extreme weight loss and thinness due to a lack of nutrition or disease, leading to visible depletion of body fat and muscle.

Companionate Love

A form of love characterized by deep affection, mutual respect, and a strong bond that develops over time.

Affection And Trust

Fundamental components of close relationships, involving feelings of warmth and fondness towards another, and belief in their reliability and support.

Crop Failures

Instances where agricultural crops do not grow as expected due to factors such as drought, pests, disease, or extreme weather, leading to a significant loss in yield.