求(x^(1/5)-1)/(x-1)在x趋向于1时的极限
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求(x^(1/5)-1)/(x-1)在x趋向于1时的极限
求(x^(1/5)-1)/(x-1)在x趋向于1时的极限
求(x^(1/5)-1)/(x-1)在x趋向于1时的极限
令t=x^(1/5)
则x=t^5
分解因式
t^5-1=(t-1)(t^4+t^3+t^2+t+1)
所以,原式=1/(t^4+t^3+t^2+t+1)
当x趋近1时,t也趋近1
故结果为1/5
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