题目
underset(lim)(x→0)dfrac(arctanx-x)(ln(1+2{x)^3)}= ____ ．
$\underset{lim}{x→0}$$\dfrac{arctanx-x}{ln(1+2{x}^{3})}$
=
____ ．题目解答
答案
解：原式=$\underset{lim}{x→0}$$\dfrac{\dfrac{1}{1+{x}^{2}}-1}{\dfrac{6x}{1+{2x}^{3}}}$=$\underset{lim}{x→0}$$\dfrac{-x-2{x}^{4}}{6+6{x}^{2}}$=0，
故答案为：0．