极限求解答,需要过程,谢谢
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(x->1) lim (x³-3x²+2)/(x³-x²-x+1)
=(x->1) lim [(x-1)x²-2(x²-1)]/[(x²(x-1)-(x-1)]
=(x->1) lim (x-1)(x²-2x-2)/[(x-1)(x²-1)]
=(x->1) lim [(x-1)²-3)]/[(x-1)(x+1)]
=(x->1) lim (x-1)/(x+1)-3/[(x-1)(x+1)]
=0 - (x->1) lim 3/[(x-1)(x+1)]
分母是无穷小量,分式是无穷大量,原式无极限
=(x->1) lim [(x-1)x²-2(x²-1)]/[(x²(x-1)-(x-1)]
=(x->1) lim (x-1)(x²-2x-2)/[(x-1)(x²-1)]
=(x->1) lim [(x-1)²-3)]/[(x-1)(x+1)]
=(x->1) lim (x-1)/(x+1)-3/[(x-1)(x+1)]
=0 - (x->1) lim 3/[(x-1)(x+1)]
分母是无穷小量,分式是无穷大量,原式无极限
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