Solve this :

Q .   Check   continuity   for   the   following   sin   cos   x 1 +   cos   x                                         x   0                   0                                                                 x = 0 Where     denotes   Greatest   Integer   Function

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

fx=sincosx1+cosxx00x=0We have f0=0NowL.H.L.=limx0- fx=limx0-sincosx1+cosxNow cos0=1 but as we move left of x=0, then value of cosx becomesless than 1 which means cosx=0 As X=0 if 0X<1limx0-sincosx1+cosx=sin01+0=0R.H.L.=limx0+ fx=limx0+sincosx1+cosxNow cos0=1 but as we move right of x=0, then value of cosx becomesless than 1 which means cosx=0 As X=0 if 0X<1limx0+sincosx1+cosx=sin01+0=0Hencelimx0- fx=limx0+ fx=f0=0Hence function is continuous at x=0

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.

  • 0
What are you looking for?