limx->0 5x/(1+x)^(1/3)-(1-x)^(1/3)

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 19:13:17

limx->0 5x/(1+x)^(1/3)-(1-x)^(1/3)
limx->0 5x/(1+x)^(1/3)-(1-x)^(1/3)

limx->0 5x/(1+x)^(1/3)-(1-x)^(1/3)
5x/((1+x)^(1/3)-(1-x)^(1/3))
=5x*((1+x)^(2/3) + (1-x)^(2/3) +(1-xx)^(1/3)) / ((1+x)^(1/3)-(1-x)^(1/3))((1+x)^(2/3) + (1-x)^(2/3) +(1-xx)^(1/3))
=5x*((1+x)^(2/3) + (1-x)^(2/3) +(1-xx)^(1/3)) / 2x
=5/2 * ((1+x)^(2/3) + (1-x)^(2/3) +(1-xx)^(1/3))
而
（limx->0）((1+x)^(2/3) + (1-x)^(2/3) +(1-xx)^(1/3))
=((1+0)^(2/3) + (1-0)^(2/3) +(1-0)^(1/3))
=3
原式=15/2