Limited yet powerful (VIII)

Calculus Level 4

limx0(ex2/2cosx)1/x4 \large \lim_{x\to 0} (e^{x^2 /2} \cos x)^{1/x^4}

If the value of the limit above is equal to ea/b e^{-a/b} , where aa and bb are coprime positive integers, find the value of a+ba+b.

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