Estimate the error in the quadratic approximation of the given function at the origin over the given region.
-$$f ( x , y ) = \sin 3 x \sin ^ { 2 } 4 y , | x | \leq 0.1 , | y | \leq 0.1$$
A) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.018$
B) $| E ( x , y ) | \leq 0.064$
C) $| E ( x , y ) | \leq 0.256$
D) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.0853$

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The Answer of Estimate the error in the quadratic approximation of the given function at the origin over the given region.
-$$f ( x , y ) = \sin 3 x \sin ^ { 2 } 4 y , | x | \leq 0.1 , | y | \leq 0.1$$
A) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.018$
B) $| E ( x , y ) | \leq 0.064$
C) $| E ( x , y ) | \leq 0.256$
D) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.0853$

Estimate the Error in the Quadratic Approximation of the Given f(x,y)=sin⁡3xsin⁡24y,∣x∣≤0.1,∣y∣≤0.1f ( x , y ) = \sin 3 x \sin ^ { 2 } 4 y , | x | \leq 0.1 , | y | \leq 0.1f(x,y)=sin3xsin24y,∣x∣≤0.1,∣y∣≤0.1

Estimate the Error in the Quadratic Approximation of the Given $f ( x , y ) = \sin 3 x \sin ^ { 2 } 4 y , | x | \leq 0.1 , | y | \leq 0.1$