高等数学中带参数的极限问题

两边除以x

left = lim[(1+x2+x3)(1/3)-ax-b]/x

=lim[(1+x^2+x^3)^(1/3)-ax]/x

=lim(1/x^3+1/x+1)^(1/3)-a

=1-a

=0=右

a=1

代入a=1，分子按三次差分公式组织。

b=lim(1+x^2+x^3)^(1/3)-x

= lim(1+x2+x3-x3)/[(1+x2+x3)(2/3)+x(1+x2+x3)(。

=lim(1/x^2+1)/[(1/x^3+1/x+1)^(2/3)+(1/x^3+1/x+1)^(1/3)+1]

=1/3