Use Taylor's Formula to Find the Requested Approximation of F(x $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \frac { 1 } { 1 + 4 \mathrm { x } + \mathrm { y } }$

question 46

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Cubic approximation to $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \frac { 1 } { 1 + 4 \mathrm { x } + \mathrm { y } }$

• A) \(1 - 4 x - y + 16 x ^ { 2 } + 8 x y + y ^ { 2 } - 64 x ^ { 3 } + 48 x ^ { 2 } y - 12 x y ^ { 2 } + y ^ { 3 }\)
• B) \(1 - 4 x - y + 16 x ^ { 2 } + 8 x y + y ^ { 2 } - 64 x ^ { 3 } - 48 x ^ { 2 } y - 12 x y ^ { 2 } - y ^ { 3 }\)
• C) \(1 - 4 x - y + 16 x ^ { 2 } + 4 x y + y ^ { 2 } - 64 x ^ { 3 } + 48 x ^ { 2 } y - 12 x y ^ { 2 } + y ^ { 3 }\)
• D) \(1 - 4 x - y + 16 x ^ { 2 } + 4 x y + y ^ { 2 } - 64 x ^ { 3 } - 48 x ^ { 2 } y - 12 x y ^ { 2 } - y ^ { 3 }\)

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