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:

Homeostasis

The ideal level of bodily functions.

Walter Cannon

A physiologist known for his work on the "fight or flight" response and for coining the term homeostasis.

General Adaptation Syndrome

Selye’s stage theory of how we respond to all stressors in a similar way.

Physiological Damage

Harm or injury to the body's structures or functions resulting from disease, trauma, or other factors.