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

question 86

Multiple Choice

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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