Mathematics, 03.07.2019 08:00 natalie3734
Find a function ω(x) such that the function f(x) = sin(ω(x)) has the roots at π, π2 , π3 , ..
Answers: 1
![f(x)=\sin(\omega(x))\\\\f(\pi^n)=\sin(\omega(\pi^n))=0, n\in\mathbb{N}\\\\\\\sin x=0 \implies x=k\pi,k\in\mathbb{Z}\\\Downarrow\\\omega(\pi^n)=k\pi\\\\\boxed{\omega(x)=k\sqrt[\log_{\pi} x]{x},k\in\mathbb{Z}}](/tpl/images/0045/6445/90c14.png)
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Find a function ω(x) such that the function f(x) = sin(ω(x)) has the roots at π, π2 , π3 , .....
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