Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { ( 1 + x + 6 y ) ^ { 2 } }$

question 54

Multiple Choice

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

• A) \(1 + 2 x + 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }\)
• B) \(1 + 2 x + 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }\)
• C) \(1 - 2 x - 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }\)
• D) \(1 - 2 x - 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }\)

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