If f(x) =  and Rd denotes the right hand derivative of f(x) at x = I, then  is

Dear Student,
Please find below the solution to the asked query:

R.H.D. is given byRd=limxI+ fx-fIx-IGiven that fI=0Rd=limxI+ fxx-I=limxI+ 1-cos2πxxx-I=limxI+ 1-cos2πxx-xx-I As x=x-xFor x is slightly greater than 1, hence x=I=limxI+ 1-cos2πxx-Ix-I=limxI+1-cos2πxx-I2For 00 form L-Hopital rule can be applied, hence differentiate with respect to xRd=limxI+ sin2πx2π2x-IAs sine is 0 at integral multiple of π, hence still it is 00 form. Again DifferentiateRd=limxI+ cos2πx4π22=limxI+ cos2πx2π2Apply limt=cos22π2Rd=2π2 As cos2=1Rdπ2=2 Answer

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 0
Rd/pie^2 =1
  • 0
how??
  • 0
What are you looking for?