Question

limita cand x tinde la 0 din (radical din 1 - cos x patrat )/(1-cosx)

Answer 1

Răspuns:

$\lim _{x\to 0}\left(\frac{\sqrt{1}-cosx^2}{1-cosx}\right)=0$

Explicație pas cu pas:

$\lim _{x\to 0}\left(\frac{\sqrt{1}-cosx^2}{1-cosx}\right)=\\\\\lim _{x\to 0}\left(\frac{1-cosx^2}{1-cosx}\right)=\\\\\lim _{x\to 0}\left(\frac{2xsinx^2}{sinx}\right)=\\\\\lim _{x\to 0}\left(\frac{2(sinx^2+2x^2cosx^2)}{cosx}\right)=\\\\\lim _{x\to 0}\left(\frac{2(sin0^2+2*0^2cos0^2)}{cos0}\right)= 0$

Succes! :)