Find the second-order Taylor polynomial T2(x,y)T_2(x,y)T2(x,y) for f(x,y)=sin(xy)f(x,y) = \sin(xy)f(x,y)=sin(xy) centered at (0,0)(0, 0)(0,0).
xyxyxy
xy−(xy)36xy - \frac{(xy)^3}{6}xy−6(xy)3
1−(xy)221 - \frac{(xy)^2}{2}1−2(xy)2
xy+(xy)22xy + \frac{(xy)^2}{2}xy+2(xy)2