请教一道极限的计算题求(x,y)趋近于(0,0)时,lim(sin(xy)+xycosx-(x^2)(y^2))/x 不要光有答案)

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请教一道极限的计算题
求(x,y)趋近于(0,0)时,lim(sin(xy)+xycosx-(x^2)(y^2))/x 不要光有答案)

lim[(x,y)->(0,0)] (sin(xy)+xycosx-(x^2)(y^2))/x
= lim[(x,y)->(0,0)] sin(xy)/x
+lim[(x,y)->(0,0)] xycosx/x
+lim[(x,y)->(0,0)] (x^2)(y^2)/x
= lim[(x,y)->(0,0)] sin(xy)/xy * y
+lim[(x,y)->(0,0)] ycosx
+lim[(x,y)->(0,0)] x*(y^2)
= 1*0+0*1+0*0=0