Find the Area of the Surface $$\mathbf { r } ( u , v ) = ( 5 u + 3 v + 4 ) \mathbf { i } + ( 2 u + 3 v + 4 ) \mathbf { j } + ( 4 u + 2 v + 8 ) \mathbf { k }$$

question 16

Multiple Choice

Find the area of the surface. The part of the plane $$\mathbf { r } ( u , v ) = ( 5 u + 3 v + 4 ) \mathbf { i } + ( 2 u + 3 v + 4 ) \mathbf { j } + ( 4 u + 2 v + 8 ) \mathbf { k }$$ ; $0 \leq u \leq 1$ , $0 \leq v \leq 5$

• A) \(5 \sqrt { 149 }\)
• B) \(\sqrt { 58 }\)
• C) \(\sqrt { 51 }\)
• D) \(2 \sqrt { 11 }\)

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Definitions:

Loose Associations

A common thinking disturbance in schizophrenia, characterized by rapid shifts from one topic of conversation to another. Also known as derailment.

Digressive Language

Language that deviates or diverges from the main topic or line of argument.

Schizotypal Personality Disorder

A psychiatric condition marked by intense fear of social interactions, disturbed thoughts, paranoia, feelings of unreality, temporary psychotic episodes, and frequently, unusual beliefs.

Antisocial Personality Disorder

A psychological state characterized by a persistent disregard for morality and indifference to the rights and emotions of others.