Sequence/Rational and trigonometric/2/Exercise

Decide whether the sequence defined by

${}x_{n}:={\frac {5\sin ^{3}n-6n^{4}+13n^{2}+{\left(\sin n\right)}{\left(\cos {\left(n^{2}\right)}\right)}}{7n^{4}-5n^{3}+n^{2}\sin ^{2}{\left(n^{3}\right)}-\cos n}}\,$

converges in ${}\mathbb {R}$ and determine, if applicable, the limit.

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