$$\mathop {Lim}\limits_{x \to \infty } {{{x^3} - \cos x} \over {{x^2} + {{\left( {\sin x} \right)}^2}}} = \_\_\_\_\_\_.$$

The value of the double integral $$\int\limits_0^1 {\int\limits_x^{{1 \over x}} {{x \over {1 + {y^2}}}\,\,dx\,\,dy = \_\_\_\_\_.} } $$