The function $$f(x)=$$ $$sin$$$$π$$xn!$$-$$$$cos$$$$π$$$$x(n+1)$$! is

Correct option is 3periodic with period 2 (n + 1)!

Questions

The function $f (x) = \sin (\frac{πx}{n!}) - \cos \frac{πx}{(n + 1)!}$ is

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non periodic

periodic with period 2(n!)

periodic with period 2 (n + 1)!

periodic with period n!

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detailed solution

Correct option is C

Since the period of sin x is 2π so the period of sin πxn! is 2πn!π=2(n!) The period of cosπx(n+1)! is 2(n+1)! The period of f(x)=1.c.m (2n!),2(n +1)!=2(n+1)!

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The function f(x)= sinπxn!-cosπx(n+1)! is

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The function $f (x) = \sin (\frac{πx}{n!}) - \cos \frac{πx}{(n + 1)!}$ is