# 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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