Ludicrous Limit

Calculus Level 3

The function \(f:\Bbb R^2\to \Bbb R\) is defined as \[f(a,b)=\lim_{x\to\infty}\left(\frac{a^{1/x}+b^{1/x}}2\right)^x\] Find the value of \(f(12, 3)\).

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