Estimate the Error in the Quadratic Approximation of the Given $f ( x , y ) = \sin 5 x \sin 2 y , | x | \leq 0.1 , | y | \leq 0.1$

question 409

Multiple Choice

Estimate the error in the quadratic approximation of the given function at the origin over the given region.
- $f ( x , y ) = \sin 5 x \sin 2 y , | x | \leq 0.1 , | y | \leq 0.1$

• A) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.25\)
• B) \(| E ( x , y ) | \leq 0.1667\)
• C) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.125\)
• D) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.5\)

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Definitions:

Internal Factor

Psychological or physiological conditions within an individual that influence their behaviors and decisions.

External Factor

Influences that impact an individual or organization but originate outside of their control.

Illusion of Control

The erroneous belief that one can influence or control outcomes that are actually determined by chance.

Discounting Principle

A psychological concept suggesting that when there are multiple perceived causes for behaviour, the importance of any single cause is diminished.