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

Multiple Choice

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) $| E ( x , y ) | \leq 0.1707$