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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