Question

Să se afle lim x->0 (x-arctgx)/x³.

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\lim_{x\to 0}\dfrac{x-\arctan x}{x^3}\stackrel{\frac{0}{0}}{=}\lim_{x\to 0}\dfrac{1-\frac{1}{x^2+1}}{3x^2}=\lim_{x\to 0}\dfrac{\frac{x^2}{x^2+1}}{3x^2}=\lim_{x\to 0}\dfrac{1}{3(x^2+1)}=\boxed{\dfrac{1}{3}}$