periodic

1.
Is cos x² a periodic function ?

2. Find the fundamental period of the function 2cos x-Ï€3

2 Answers

cos((x+T)^{2})=cos(x^{2})

\Rightarrow (x+T)^{2}= 2n\pi\;\pm x^{2}

\Rightarrow x^{2}+T^{2}+2Tx= 2n\pi\;\pm x^{2}

\Rightarrow T^{2}+2Tx= 2n\pi

OR
T^{2}+2Tx+ 2x^{2}= 2n\pi

in boh cases , we wont be able to find T independent of x , hence T isnt a constant ,

thus cos(x²) isnt periodic ,

2.6\pi

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