Scary Limits!!

Calculus Level 4

β\beta =limx(2xn)1/ex(3xn)1/exxn \displaystyle \lim_{ x \rightarrow \infty} \dfrac{(2^{x^n})^{{1}/{e^x}} -(3^{x^n})^{{1}/{e^x}} }{x^n}

Given That n ϵ\epsilon N.

Find 2β+2β+12^{\beta} + 2^{\beta +1}.

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