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求极限limx 1时 根号3次方x -1/根号x -1等于多少(求化简详细过程)
题目详情
求极限limx 1时 根号3次方x -1/根号x -1等于多少(求化简详细过程)
▼优质解答
答案和解析
lim(x→1)[x^(1/3) -1]/(√x -1)
=lim(x→1)[x^(1/3) -1][x^(2/3)+x^(1/3)+1](√x +1)/[x^(2/3)+x^(1/3)+1](√x -1)(√x +1)
=lim(x→1)(√x +1)/[x^(2/3)+x^(1/3)+1]
=(1+1)/1+1+1)=2/3
=lim(x→1)[x^(1/3) -1][x^(2/3)+x^(1/3)+1](√x +1)/[x^(2/3)+x^(1/3)+1](√x -1)(√x +1)
=lim(x→1)(√x +1)/[x^(2/3)+x^(1/3)+1]
=(1+1)/1+1+1)=2/3
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