lim=(x²-y²-2x+2y)/(x+ y-2) ① （x,y)→（2,0） ②（x,y)→（0,2） 极限怎么求

lim=(x²-y²-2x+2y)/(x+ y-2) ① （x,y)→（2,0） ②（x,y)→（0,2） 极限怎么求

lim(x,y)→(2,0) (x²-y²-2x+2y) / (x+y-2)
= lim (x²+xy-2x -xy-y²+2y) / (x+y-2)
= lim [x(x+y-2)-y(x+y-2)] / (x+y-2)
= lim [(x-y)(x+y-2)] / (x+y-2)
= lim (x-y)
= 2 - 0
= 2