Find the Area of the Surface $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k } ; 0 \leq u \leq 3,0 \leq v \leq 2 \pi$

question 92

Multiple Choice

Find the area of the surface.
The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k } ; 0 \leq u \leq 3,0 \leq v \leq 2 \pi$

• A) \(\frac { 5 \pi ( 37 \sqrt { 37 } - 1 ) } { 12 }\)
• B)
• \(\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 6 }\)
• C) \(\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 12 }\)
• D) \(\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 3 }\)

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Definitions:

Treisman's Experiments

Groundbreaking psychological experiments conducted by Anne Treisman that explored the nature of attention, particularly through the feature integration theory.

Feature Integration

Feature integration theory is a psychological theory concerning how an individual combines visual features to perceive objects as unified wholes.

Sensory Neglect

A condition often resulting from brain damage where an individual ignores stimuli on one side of their body or the space around them.

Parietal Lobe

A region of the cerebral cortex involved in processing sensory information regarding the location of parts of the body as well as interpreting visual information and processing language and mathematics.