求極限lim(x^2y^2)/「x^2+y^2+(x-y)^2」(x,y)趨向於0

求極限lim(x^2y^2)/「x^2+y^2+(x-y)^2」(x,y)趨向於0

設沿著y = kx這條直線趨近於原點,則有:lim(x^2 *y^2)/[x^2 + y^2 +(x - y)^2]=lim(k^2 *x^4)/[x^2 + k^2 *x^2 +(k -1)^2 * x^2]=lim k^2 *x^2 /[1 + k^2 +(k -1)^2 ]=lim k^2 * 0^2 /[1 + k^2 +(k -1)^2 ]…