Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to $f ( x , y ) = \frac { 1 } { 1 + 6 x + y }$
A) $1 - 6 x - y + 36 x ^ { 2 } + 6 x y + y ^ { 2 }$
B) $1 - 6 x - y + 36 x ^ { 2 } + 12 x y + y ^ { 2 }$
C) $1 + 6 x + y + 36 x ^ { 2 } + 12 x y + y ^ { 2 }$
D) $1 + 6 x + y + 36 x ^ { 2 } + 6 x y + y ^ { 2 }$

Question

Quizplus · Accepted Answer

The quadratic approximation of a function using Taylor's formula involves calculating the first and second partial derivatives at the origin and using them to form the approximation. For $f(x, y) = \frac{1}{1 + 6x + y}$, the correct quadratic approximation is $1 - 6x - y + 36x^2 + 12xy + y^2$.

Use Taylor's Formula to Find the Requested Approximation of F(x f(x,y)=11+6x+yf ( x , y ) = \frac { 1 } { 1 + 6 x + y }f(x,y)=1+6x+y1​

Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { 1 + 6 x + y }$