one root of the equation cosx- x+1/2=0 lies in the interval 0 to π/2.prove

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

We have:fx=cosx-x+12Nowf0=cos0-0+12=1+12=32f0>0fπ2=cosπ2-π2+12=0+1-π2=1-π2fπ2<0As f0>0 and fπ2<0, hence there will exist atleast one root offx in x0,π2 as fx will cross X-axis when it changes from positive to negative.

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.

  • 3
What are you looking for?