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  • If [x] denote the greatest integer not exceeding the real number x, then the period of the function f(x)=sin [pi^2] x+sin [-pi^2]x, is

If [x] denote the greatest integer not exceeding the real number x, then the period of the function f(x)=sin [pi^2] x+sin [-pi^2]x, is

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Solution:      pi^2=9.87Rightarrow [pi^2]=9.   Similarly,

                     -pi^2=-9.87Rightarrow [-pi^2]=-10.

                  herefore        f(x)=sin 9pi x-sin 10 pi x      .........(1)

                    pd(sin 9pi x)=frac2pi9;    and    pd(sin 10pi x)=frac2pi10.

                herefore        pd(f)=fracLCM2pi,2piHCM9,10=2pi 

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Deependra Verma

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