Estimate the error in the quadratic approximation of the given function at the origin over the given region.
-$$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$
A) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.1422$
B) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.2327$
C) $| E ( x , y ) | \leq 0.012$
D) $| E ( x , y ) | \leq 0.1707$

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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.
-$$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$
A) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.1422$
B) $| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.2327$
C) $| E ( x , y ) | \leq 0.012$
D) $| E ( x , y ) | \leq 0.1707$

Estimate the Error in the Quadratic Approximation of the Given f(x,y)=ln⁡(1+3x+4y),∣x∣≤0.1,∣y∣≤0.1f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1f(x,y)=ln(1+3x+4y),∣x∣≤0.1,∣y∣≤0.1

Estimate the Error in the Quadratic Approximation of the Given $f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$