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  • If [x] denotes the greatest integer not exceeding the real number x, then the number of points of discontinuities of the function f(x)=[sinx+cosx] , 0

If [x] denotes the greatest integer not exceeding the real number x, then the number of points of discontinuities of the function f(x)=[sinx+cosx] , 0

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Solution:    The given function can be written as

                                           f(x)=sqrt2[sin (x+fracpi4)]

                    For      0< x< 2pi,  the function   sin (x+fracpi4)   has integral

                   values at the points    fracpi4,frac3pi4,frac5pi4   and   frac7pi4.

                  Therefore ,  f(x)  has discontinuities at four points.

Posted by

Deependra Verma

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