Calculate the second-order Taylor polynomial for f(x,y)=cos(x+y)f(x, y) = \cos(x+y)f(x,y)=cos(x+y) centered at (0,0)(0, 0)(0,0).
1−12(x+y)21 - \frac{1}{2}(x+y)^21−21(x+y)2
1−x2−y21 - x^2 - y^21−x2−y2
1−12x2−12y21 - \frac{1}{2}x^2 - \frac{1}{2}y^21−21x2−21y2
1−x−y−12(x+y)21 - x - y - \frac{1}{2}(x+y)^21−x−y−21(x+y)2