Use Taylor's Formula to Find the Requested Approximation of F(x $10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } y ^ { 2 }$

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to f(x, y) = sin(10x + y)

A) $10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } y ^ { 2 }$
B) $10 x + y + 5 x ^ { 2 } + \frac { 1 } { 2 } x y + \frac { 1 } { 2 } y ^ { 2 }$
C) $10 x + y$
D) $10 x + y + 5 x ^ { 2 } + y ^ { 2 }$