# Eta BEta

Calculus Level 3

Let $$f(x) =k\cos x$$. If the sum of coefficients of $$\cos x$$ in the expansion of $$\left(1+f(x)\right)^n$$ is $$\eta$$ and the sum of coefficients of $$\sin x$$ in the expansion of $$\left(1+\dfrac {df(x)}{dx}\right)^n$$ is $$\beta$$, find

$\large \lim_{n\to\infty} \frac{|\eta\beta|}{\left(|\eta\beta|^{1/n}+1\right)^n}.$

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