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Consider the Top Half of the Ellipsoid x2+y2+14z2=1,z0x ^ { 2 } + y ^ { 2 } + \frac { 1 } { 4 } z ^ { 2 } = 1 , z \geq 0

question 137

Short Answer

Consider the top half of the ellipsoid x2+y2+14z2=1,z0x ^ { 2 } + y ^ { 2 } + \frac { 1 } { 4 } z ^ { 2 } = 1 , z \geq 0 parametrized by x=sinusinv,y=cosusinv,z=2cosv,0vπ2x = \sin u \sin v , y = \cos u \sin v , z = 2 \cos v , 0 \leq v \leq \frac { \pi } { 2 } . Find a normal vector N at the point determined by u=π4,v=π3u = \frac { \pi } { 4 } , v = \frac { \pi } { 3 } , and determine if it is upward and/or outward.

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Definitions:

Anima

In Jungian psychology, the unconscious feminine side of a man or the masculine aspects in a woman, often manifested in dreams or creative activities.

Animus

In Jungian psychology, the animus refers to the unconscious masculine side of a woman.

Psychological Types

A concept developed by Carl Jung that categorizes individuals according to their primary mode of psychological functioning.

Extraverted Thinking

A cognitive function described in Jungian psychology that focuses on external objects and operates through objective and logical reasoning.

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