If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value

The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.

$$\mathop {Lim}\limits_{\theta \to 0} \,{{\sin \,m\,\theta } \over \theta },$$ where $$m$$ is an integer, is one of the following :

$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle x$}} = \_\_\_\_\_.$$