The period of f(x) = cos left(frac{x}{3}right | vedclass

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(D) Given function is $f(x) = \cos \left(\frac{x}{3}\right) + \sin \left(\frac{x}{2}\right)$.We know that the period of $\cos(ax)$ is $\frac{2 \pi}{|a

Vedclass · Accepted Answer

$12$

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(D) Given function is $f(x) = \cos \left(\frac{x}{3}ight) + \sin \left(\frac{x}{2}ight)$.We know that the period of $\cos(ax)$ is $\frac{2 \pi}{|a|}$ and the period of $\sin(bx)$ is $\frac{2 \pi}{|b|}$.For the first term $\cos \left(\frac{x}{3}ight)$, the period $T_1 = \frac{2 \pi}{1/3} = 6 \pi$.For the second term $\sin \left(\frac{x}{2}ight)$, the period $T_2 = \frac{2 \pi}{1/2} = 4 \pi$.The period of the sum of two periodic functions is the Least Common Multiple $(LCM)$ of their individual periods.Therefore, the period of $f(x) = 	ext{LCM}(6 \pi, 4 \pi)$.Since $6 \pi = 2 	imes 3 \pi$ and $4 \pi = 2 	imes 2 \pi$, the $	ext{LCM}(6 \pi, 4 \pi) = 12 \pi$.Thus, the period of $f(x)$ is $12 \pi$.

The period of $f(x) = \cos \left(\frac{x}{3}\right) + \sin \left(\frac{x}{2}\right)$ is (in $\pi$)

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