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

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) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.5$