Find the second order Taylor approximation t o f ( x , y ) e x 4 y ) a t the point ( x 0 , y 0 ) ( 0 , 0 ) Select your answer from the options listed g ( x , y ) 1 x y 1 2 x 2 x y 1 2 y 2 g ( x , y ) 1 x 4 y 1 2 x 2 4 x y 8 y 2 g ( x , y ) 1 x 4 y 1 2 x 2 4 x y 8 y 2 g ( x , y ) 1 x y 1 2 x 2 x y 1 2 y 2 g ( x , y ) 1 x 2 y 1 2 x 2 2 x y 4 y 2

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Question: Find the second - order Taylor approximation t o { : f ( x , y ) = e x + 4 y ) a

Find the second

-

order Taylor approximation

t o

{

f (x, y) = e^{x + 4 y}) a t

the point

(x_{0}, y_{0}) = (0, 0) .

Select your answer from the options listed.

g (x, y) = 1 + x + y + \frac{1}{2} x^{2} - x y + \frac{1}{2} y^{2}

g (x, y) = 1 + x + 4 y + \frac{1}{2} x^{2} + 4 x y + 8 y^{2}

g (x, y) = 1 + x + 4 y + \frac{1}{2} x^{2} - 4 x y + 8 y^{2}

g (x, y) = 1 + x + y + \frac{1}{2} x^{2} + x y + \frac{1}{2} y^{2}

g (x, y) = 1 + x + 2 y + \frac{1}{2} x^{2} + 2 x y + 4 y^{2}

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