# Cos the limit is funny

Calculus Level 3

$\begin{eqnarray} f(x) &=& \dfrac{1-\cos(1-\cos x)}{x^4} , x \neq 0 \\ f(0) &=& a \end{eqnarray}$

The function $$f(x)$$ is defined as above. If $$f(x)$$ is continuous everywhere, then $$a$$ is equal to $$\dfrac{A}{B}$$ for coprime positive integers $$A$$ and $$B$$, find $$A+B$$.

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