Use Taylor's Formula to Find the Requested Approximation of F(x

question 193

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Cubic approximation to f(x, y) = ln(1 + 7x + y)

• A) \(1 + 7 x + y - \frac { 49 } { 2 } x ^ { 2 } - 7 x y - \frac { 1 } { 2 } y ^ { 2 } + \frac { 343 } { 3 } x ^ { 3 } + \frac { 49 } { 3 } x ^ { 2 } y + \frac { 7 } { 3 } x y ^ { 2 } + \frac { 1 } { 3 } y ^ { 3 }\)
• B) \(7 x + y - \frac { 49 } { 2 } x ^ { 2 } - 7 x y - \frac { 1 } { 2 } y ^ { 2 } + \frac { 343 } { 3 } x ^ { 3 } + \frac { 49 } { 3 } x ^ { 2 } y + \frac { 7 } { 3 } x y ^ { 2 } + \frac { 1 } { 3 } y ^ { 3 }\)
• C) \(1 + 7 x + y - \frac { 49 } { 2 } x ^ { 2 } - 7 x y - \frac { 1 } { 2 } y ^ { 2 } + \frac { 343 } { 3 } x ^ { 3 } + 49 x ^ { 2 } y + 7 x y ^ { 2 } + \frac { 1 } { 3 } y ^ { 3 }\)
• D) \(7 x + y - \frac { 49 } { 2 } x ^ { 2 } - 7 x y - \frac { 1 } { 2 } y ^ { 2 } + \frac { 343 } { 3 } x ^ { 3 } + 49 x ^ { 2 } y + 7 x y ^ { 2 } + \frac { 1 } { 3 } y ^ { 3 }\)

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