Răspuns:
[tex]\lim _{x\to 0}\left(\frac{\sqrt{1}-cosx^2}{1-cosx}\right)=0[/tex]
Explicație pas cu pas:
[tex]\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[/tex]
Succes! :)
