分子有理化
原式=(-x-8)/[(2+x^(1/3))((1-x)^(1/2)+3)]
=-(2+x^(1/3))*(4+x^(2/3)-2x^(1/3))/[(2+x^(1/3))((1-x)^(1/2)+3)]
=-(4+x^(2/3)-2x^(1/3)/((1-x)^(1/2)+3)
x趨近于-8
原式=-2
分子分母構(gòu)成0/0型極限
用洛必達法則
原式=分子的導(dǎo)數(shù)/分母的導(dǎo)數(shù)
=[(-1/2)*(1-x)^(1/2)]/[(1/3)*x^(-2/3)]
x趨近于-8
原式=-2