Răspuns:
Explicație pas cu pas:
[tex]\displaystyle\lim_{x\to 0}\dfrac{x-\arctan x}{x^3}\stackrel{\frac{0}{0}}{=}\lim_{x\to 0}\dfrac{1-\frac{1}{x^2+1}}{3x^2}=\lim_{x\to 0}\dfrac{\frac{x^2}{x^2+1}}{3x^2}=\lim_{x\to 0}\dfrac{1}{3(x^2+1)}=\boxed{\dfrac{1}{3}}[/tex]