According to the mean value theorem of double integral, there exists a point (x 1, y 1) and (x 1) 2+(y 1) 2.

Original formula = lim (rou->; 0+)[( 1/(pai*(rou)^2))*e^((x 1)^2-(y 1)^2)*cos(x 1+y 1)*pai*(rou)^2]=lim(rou->； 0+)[e^((x 1)^2-(y 1)^2)*cos(x 1+y 1)]

Obviously when rou-& gt；; 0+，x 1->； 0，y 1->； 0, so the original formula = 1.