$$\mathop {\lim }\limits_{x \to \infty } {{x - \sin x} \over {x + \cos \,x}}\,\,Equals$$

Consider the following two statements about the function $$$f\left( x \right) = \left| x \right|:$$$

$$P.\,\,f\left( x \right)$$ is continuous for all real values of $$x$$
$$Q.\,\,f\left( x \right)$$ is differentiable for all real values of $$x$$

Which of the following is True?

$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$

The value of the integral is $${\rm I} = \int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} {{{\cos }^2}x\,dx} $$