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If f(x)=lim(n to oo)sin^(4)x+1/4sin^(4)2...

If `f(x)=lim_(n to oo)sin^(4)x+1/4sin^(4)2x+..=1/(4^(n)).sin^(4)(2^(n)x)` and `g(x)` is a differentiable function satisfying `g(x)+f(x)=1`, then the maximum value of `(sqrt(f(x))+sqrt(g(x)))^(4)` is ……….

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