Estimate the Error in the Quadratic Approximation of the Given $f ( x , y ) = e ^ { 4 x } \sin y , | x | \leq 0.1 , | y | \leq 0.1$

question 400

Multiple Choice

Estimate the error in the quadratic approximation of the given function at the origin over the given region.
- $f ( x , y ) = e ^ { 4 x } \sin y , | x | \leq 0.1 , | y | \leq 0.1$

• A) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.0955\)
• B) \(| E ( x , y ) | \leq 0.191\)
• C) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.3819\)
• D) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.1273\)

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Definitions:

Hydrazone Derivative

A compound resulting from the reaction of a hydrazine with a carbonyl group, typically in aldehydes or ketones, forming a double N=N bond.

Ketone

An organic compound characterized by a carbonyl group bonded to two carbon atoms.

Organic Product

A compound containing carbon atoms that has been formed as the result of a chemical reaction involving organic molecules.

Upper Quartile

The value above which 25% of the data or population falls, marking the upper boundary of the central 50% in a distribution.