Factorials! and a hyperbolic function

Calculus Level 4

\[\large \lim_{x \to \infty} \left(\frac {(x+2)!\cosh \left(\frac 1{\sqrt x} \right)}{x^2(x! + 1)} \right)^x = \ ? \]

Round your answer to 4 decimal places.

Notation: cosh (x) denotes the hyperbolic cosine.

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