Find the Linearization of the Function at the Given Point $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { e } ^ { 5 \mathrm { x } - 8 \mathrm { y } + 3 \mathrm { z } }$

question 30

Multiple Choice

Find the linearization of the function at the given point.
- $\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { e } ^ { 5 \mathrm { x } - 8 \mathrm { y } + 3 \mathrm { z } }$ at $( 0,0,0 )$

• A) \(L ( x , y , z ) = \frac { 5 } { 2 } x - 4 y + \frac { 3 } { 2 } z + 1\)
• B) \(L ( x , y , z ) = 5 x - 8 y + 3 z\)
• C) \(L ( x , y , z ) = 5 x - 8 y + 3 z + 1\)
• D) \(L ( x , y , z ) = \frac { 5 } { 2 } x - 4 y + \frac { 3 } { 2 } z\)

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Definitions:

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A statistical technique used to identify underlying structures (factors) that explain patterns of correlations within a set of observed variables.

Principal Components Analysis (PCA)

A statistical technique used to reduce the dimensionality of a dataset by transforming it into a set of linearly uncorrelated variables called principal components.

Factor Analysis

A statistical method used to identify underlying structures or factors among a set of observed variables by reducing data complexity.

Myth

A traditional story, especially one concerning the early history of a people or explaining some natural or social phenomenon, and typically involving supernatural beings or events.