Select Page

# Calculus – Continuity

Home Forums Math Olympiad, I.S.I., C.M.I. Entrance Calculus – Continuity

• This topic has 2 replies, 2 voices, and was last updated 1 year ago by SARA.
Viewing 3 posts - 1 through 3 (of 3 total)
• Author
Posts
• #27962
SARA
Participant

Find the number of points of discontinuity for f(x)=[6 sin x  ] ,where x lies between 0 and pi .I have got 13 points ,answer is 11 .Why is the function continuous at f(x)=0 ?

#28014
Aritra
Moderator

i think [.] denotes the greatest integer function write , other wise the problem has no meaning . now see that a floor function is dis continuous in all those integer value

([6sin(x)]) can take integer value only when (sin (x)) take the value multiple of (\frac{n}{6}) see that n= 0,1,2,3,4,5,6

now (\frac {1}{6}) can be obtained by sin x only once at the point x= (\frac{\pi}{2})

and all the value are attended twice once at 0 to\ (\frac{pi}{2}) and another  (\frac{\pi}{2}) to (\pi)  so total there are 12 point of discontinuity

i don’t think it is continuous at x=0 because at x=0 it takes a integer value and floor function is not continuous at any integer value

even the graph say that it has 12 point of discontinuity

https://www.desmos.com/calculator/wnacsak92c

please clarify if i am wrong at any point

• This reply was modified 1 year ago by Aritra.
• This reply was modified 1 year ago by Aritra.
• This reply was modified 1 year ago by Aritra.
#28196
SARA
Participant

To me clearly it seems that the number of points should be odd ,so either 11 or 13 .It is indeed 11 ,if the  point (pi/2,6) is not counted.But i am confused as to why it isn’t counted    ? If we do count it then we will have two more floors at 5 ,and so the answer will be 13 ,which is wrong .I have referred to the desmos graph .

Viewing 3 posts - 1 through 3 (of 3 total)
• You must be logged in to reply to this topic.