Question

用洛必达法则求lim(x趋于1）（x^3-3x^2+2)/(x^3-x^2-x+1)的极限，谢谢

Answer 1

lim/x→1/[(x^3-3x^2+2)/(x^3-x^2-x+1)]是lim(0/0)模型
∴由洛必达法则得原式=lim/x→1/[(3x^2-6x)/(3x^2-2x-1)]=lim/x→1/[3x(x-2)/(x-1)(3x+1)]
因为分子不为0，分母趋近于0，∴原式=∞

Answer 2

lim(x趋于1）（x^3-3x^2+2)/(x^3-x^2-x+1)
=lim(x趋于1）（3x^2-6x)/(3x^2-2x-1)
=lim(x趋于1）（6x-6)/(6x-2)
=0/4
=0.