Question

Lim стремится к 0 1-cos(x)/x*sin(x)

Answer 1

$\sin x\sim x,\,\,\, at\,\,\, x\to 0$

Answer 2

$\lim _{x\to \:0}\left(\frac{1-\cos \left(x\right)}{x\sin \left(x\right)}\right)=\lim _{x\to \:0}\left(\frac{\sin \left(x\right)}{\sin \left(x\right)+x\cos \left(x\right)}\right)= \\ \\ =\lim _{x\to \:0}\left(\frac{\cos \left(x\right)}{2\cos \left(x\right)-x\sin \left(x\right)}\right)=\frac{\cos \left(0\right)}{2\cos \left(0\right)-0\cdot \sin \left(0\right)}=\frac{1}{2}$