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Question Number 114764 by dw last updated on 21/Sep/20

$$Findperiodoff\left(x\right)=e^{{cos}^4\left(\pi x\right)+x-\lfloor x\rfloor +{cos}^2\left(\pi x\right)}$$$$$$

Answered by PRITHWISH SEN 2 last updated on 22/Sep/20

$$\mathrm{period}\mathrm{of}\cos {}^4\left(\pi \mathrm{x}\right)=1$$$$\mathrm{period}\mathrm{of}\cos {}^2\left(\pi \mathrm{x}\right)=1$$$$\mathrm{period}\mathrm{of}\mathrm{x}-\lfloor \mathrm{x}\rfloor =1$$$$\mathrm{period}\mathrm{of}\cos {}^4\pi \mathrm{x}+\mathrm{x}-\lfloor \mathrm{x}\rfloor +\cos {}^2\pi \mathrm{x}$$$$=\mathrm{L}.\mathrm{C}.\mathrm{M}(1,1,1)=1$$$$\therefore \mathrm{period}\mathrm{of}\mathrm{f}\left(\mathrm{x}\right)=1$$

Commented by dw last updated on 23/Sep/20

$${Thank}^{\prime }sSir$$

Commented by PRITHWISH SEN 2 last updated on 22/Sep/20

$$\mathrm{yes}\mathrm{you}\mathrm{are}\mathrm{right}$$

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