试确定常数a使lim[(1-x^3)^1/3-ax]=0(x趋于无穷大)
问题描述:
试确定常数a使lim[(1-x^3)^1/3-ax]=0(x趋于无穷大)
答
[(1-x^3)^1/3-ax]=x[-a-(1-1/x^3)^(1/3)],
由(1-1/x^3)^(1/3)∽1-1/(3x^3),
若lim[(1-x^3)^1/3-ax]=0,则-a-1=0,得a=-1.