Question

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

Answer 1

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