求极限limx→∞[(x+1)2/3-(x-1)2/3].
limx→∞[(x+1)2/3-(x-1)2/3] =limxx→∞1/3[(x+1)1/3+(x-1)1/3]•[(x+1)1/3-(x-1)1/3] =limxx→∞1/3[(x+1)+(x-1)}1/3]. [(x+1)-(x-1)]/[(x+1)2/3+(x+1)1/3•(x-1)1/3+(x-1)2/3] =2limx→∞x1/3•[(x+1)1/3+(x-1)1/3]/[(x+1)2/3+(x+1)1/3•(x-1)1/3+(x-1)2/3 =2limx→∞[(1+1/x)1/3+(1-1/x)1/3]/[(1+1/x)2/3+(1+1/x)1/3•(1-1/x)1/3+(1-1/x)1/3] =4/3