The function f(x) = x 2 + 2 x 3 - x 4 is period with period - Vidyadip

Question

The function $f(x) = \sin \frac{{\pi x}}{2} + 2\cos \frac{{\pi x}}{3} - \tan \frac{{\pi x}}{4}$ is period with period

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Answer

d
(d) Period of $\sin \frac{{\pi x}}{2} = \frac{{2\pi }}{{\pi /2}} = 4$

Period of $\cos \frac{{\pi x}}{3} = \frac{{2\pi }}{{\pi /3}} = 6$

Period of $\tan \frac{{\pi x}}{4} = \frac{\pi }{{\pi /4}} = 4$

$\therefore $Period of $f(x) = L.C.M.$ of $(4, 6, 4) = 12.$

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