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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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