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)

Question

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)

Answer 1

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