Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { ( 1 + x + 3 y ) ^ { 2 } }$

question 331

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Cubic approximation to $f ( x , y ) = \frac { 1 } { ( 1 + x + 3 y ) ^ { 2 } }$

• A) \(1 + 2 x + 6 y - 3 x ^ { 2 } - 18 x y - 27 y ^ { 2 } + 4 x ^ { 3 } + 36 x ^ { 2 } y + 108 x y ^ { 2 } + 108 y ^ { 3 }\)
• B) \(1 + 2 x + 6 y - 3 x ^ { 2 } - 24 x y - 27 y ^ { 2 } + 4 x ^ { 3 } + 36 x ^ { 2 } y + 108 x y ^ { 2 } + 108 y ^ { 3 }\)
• C) \(1 - 2 x - 6 y + 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } - 4 x ^ { 3 } - 36 x ^ { 2 } y - 108 x y ^ { 2 } - 108 y ^ { 3 }\)
• D) \(1 - 2 x - 6 y + 3 x ^ { 2 } + 24 x y + 27 y ^ { 2 } - 4 x ^ { 3 } - 36 x ^ { 2 } y - 108 x y ^ { 2 } - 108 y ^ { 3 }\)

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