Limited yet powerful (VIII)

Calculus Level 4

\[ \large \lim_{x\to 0} (e^{x^2 /2} \cos x)^{1/x^4} \]

If the value of the limit above is equal to \( e^{-a/b} \), where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).

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