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

question 81

Multiple Choice

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

• A) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 2 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } y + \frac { 4 } { 3 } x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• B) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 1 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + 1 x ^ { 2 } y + 2 x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• C) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 1 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } y + \frac { 4 } { 3 } x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)
• D) \(1 + x + 2 y + \frac { 1 } { 2 } x ^ { 2 } + 2 x y + 2 y ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + 1 x ^ { 2 } y + 2 x y ^ { 2 } + \frac { 4 } { 3 } y ^ { 3 }\)

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