Find the period of the function f(x) = \(e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}\)

Solution :

f(x) = \(e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}\)

Period of x – [x] = 1

Period of \(|cos\pi x|\) = 1

Period of \(|cos2\pi x|\) = \(1\over 2\)

……………………………….

Period of \(|cosn\pi x|\) = \(1\over n\)

So period of f(x) will be L.C.M of all period = 1.


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