limx 趋近与1 (x^(1/2)-1)/(x^(1/3)-1)

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limx 趋近与1 (x^(1/2)-1)/(x^(1/3)-1)
limx 趋近与1 (x^(1/2)-1)/(x^(1/3)-1)

limx 趋近与1 (x^(1/2)-1)/(x^(1/3)-1)
这个题目分子有理化和分母有理化
lim(x →1) (x^(1/2)-1)/(x^(1/3)-1)
=lim(x →1) (x^(1/2)-1)(x^(1/2)+1)(x^(2/3)+1+x^(1/3))/[(x^(1/2)+1)(x^(1/3)-1)(x^(2/3)+1+x^(1/3))]
=lim(x →1) (x-1)(x^(2/3)+1+x^(1/3))/[(x^(1/2)+1)(x-1)]
=lim(x →1) (x^(2/3)+1+x^(1/3))/[(x^(1/2)+1)]
=3/2