IIT JEE , AIEEE Forum - Mathematics , Trignometry - what is the period of function f(x) = x-[x] and and how it is obtained ?

studyid

what is the period of function f(x) = x-[x] and and how it is obtained ? how is it obtained
?

srini

HEY,

SINCE X-[X]={X}...I GUESS THE PERIOD IS ONE.

akhil_o

yeah thats right...
we get fractional part,which repeats at a period of 1

raulrag009

As {x}=x-[x]

where {x} denotes fractional part of x

thus

f(x)={x}

Now graph of fractional part of x repeats itself after 1 unit.

studyid

hey u are right that the period is one

but i dont understand why it is one ??

just simply bcoz it repeats after one ??

but how???

pleas state i am not able to understand ?

the actual ques. was integration from 0 to 100 of e to the power x-[x]

studyid

the thing is that i dont know how to find the period of a given function ....

studyid

can neone please explain how to find the period of a given function like that of x-[x] ?????????/

akhil_o

take a look at the graph dude...
the value the function takes repeats evry 1 unit right?
hence u can say the period is 1

studyid

is there any other method by which the period of such functions can be determined .............
some steps or manipulations.....??

akhil_o

can say for trignometric functions...others i dont know

akhil_o

for any sin ax or cos ax

the period is 2 pi/a etc

akhil_o

[],{} functions it is 1

supreet159

though their may b many other ways,it will b better 4 u to go with the graphs.this is the basic topic in maths,which is to b learnt first.
not only periods many other prob can b solved using these

srini

HEY,

WHEN DO YOU SAY A FUNCTION IS PERIODIC?...WHEN IT IS GOING TO REPEAT AFTER SOME INTERVAL...SAY FOR SOME VALUE LIKE WHEN YOU TAKE COSX,IT REPEATS AFTER 2PI ,4PI AND SO ON...THE SMALLEST VALUE AFTER WHICH A PERIODIC FUNCTION REPEATS IS CALLED ITS TIME PERIOD...LIKE FOR EXAMPLE WHEN YOU HAVE A SIMPLE PENDULUM(HYOU MUST BE LIKIN PHYSICS),ITS MOTION REPEATS AFTER SOME TIME ( WHAT WE CALL THE TIME PERIOD 'T' )THE MOTION ALSO REPEATS AFTER THE DOUBLE THE TIME AND SO ON BUT WE CALL THE SMALLEST NUMBER AS TIME PERIOD T...WE CALCULTE THIS BY

F(X+T)=F(X),WHERE F(X) IS A FUNCTION,PERIODIC,AND T IS THE TIME PERIOD.

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