Question
Let $$f\left( x \right) = \cos \,3x + \sin \,\sqrt 3 x.$$ Then $$f\left( x \right)$$ is :
A.
a periodic function of period $$2\pi $$
B.
a periodic function of period $$\sqrt 3 \pi $$
C.
not a periodic function
D.
none of these
Answer :
not a periodic function
Solution :
$$\cos \,3x$$ has the period $$\frac{{2\pi }}{3}$$ and $$\sin \,\sqrt 3 x$$ has the period $$\frac{{2\pi }}{{\sqrt 3 }}.$$
As $$\frac{{2\pi }}{3}$$ and $$\frac{{2\pi }}{{\sqrt 3 }}$$ do not have a common multiple, $$f\left( x \right)$$ is not periodic.