解：原式=lim(x->∞){[(x³+x²+x+1)-x³]/[(x³+x²+x+1)^(2/3)+x(x³+x²+x+1)^(1/3)+x²]} (分子有理化)
=lim(x->∞){(x²+x+1)/[(x³+x²+x+1)^(2/3)+x(x³+x²+x+1)^(1/3)+x²]}
=lim(x->∞){(1+1/x+1/x²)/[(1+1/x+1/x²+1/x³)^(2/3)+(1+1/x+1/x²+1/x³)^(1/3)+1]}
=(1+0+0)/(1+1+1)
=1/3。
x[(1+1/x+1/x^2+1/x^3)^(1/3)-1]
=x[1+1/3x+O(1/x^2)-1]
=1/3+O(1/x)
极限是1/3
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