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

问题描述:

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))

(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