證明函數x^2+y^2≠0時,f(x,y)=sin(xy)/√(x^2+y^2),x^2+y^2=0時f(x,y)=0在(0,0)處連續

證明函數x^2+y^2≠0時,f(x,y)=sin(xy)/√(x^2+y^2),x^2+y^2=0時f(x,y)=0在(0,0)處連續

注意:∫∫f(x,y)dxdy其實是一個常數,設a=∫∫f(x,y)dxdy則:f(x,y)=[1-(x^2+y^2)]^0.5-πa/8兩邊做二重積分得:∫∫f(x,y)dxdy積分區域為:x²;+(y-1/2)²;≤1/4,x≥0,圓的極坐標方程為:r=sinθ,θ:0--->…