求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)

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求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)令x=t^6,

求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)
求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)

求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)
令 x=t^6 ,由 x 趋于 1 得 t 趋于 1 ,
原式 = lim(t→1) [(t^2-1)/(t^3-1)]
= lim(t→1) [(t+1)(t-1)] / [(t-1)(t^2+t+1)]
= lim(t→1) (t+1)/(t^2+t+1)
= (1+1)/(1+1+1)
= 2/3 .