If f(x)= _ n ( ^4x+ 14 ^4(2x)+ + 1 4^n ^4(2^nx) ) and is differentiable and satisfies

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

f(x)=\lim_{n\to\infty}\left(\sin^4x+\frac14\sin^4(2x)+\cdots+\frac{1}{4^n}\sin^4(2^nx)\right)

and

g(x)

is differentiable and satisfies

g(x)+f(x)=1

, then the maximum value of

(\sqrt{f(x)}+\sqrt{g(x)})^4

\ldots\ldots