f(x)有定义,f(2x)=f(x)cos x,l - 知识问答

f(x)有定义,f(2x)=f(x)cos x,lim f(x)=f(0)=1(x趋于0时),求f(x)

1个回答

对任意x均有
f(x) = f(x/2)*cosx/2
= f(x/4)*cosx/2*cosx/4
=……
=∏(i = ∞)cos(x/2^i) * 1
f(x) = ∏(i = ∞)cos(x/2^i)

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