IIT JEE 1983 Maths - MCQ Question 22

Calculus Level 3

Which one of the functions is periodic?

Notation: $\lfloor \cdot \rfloor$ (in the options) denotes the floor function .

None of the others

f(x)=\sin \frac 1x

f(x)=x-\lfloor x \rfloor

f(x)=x \cos x

1 solution

Md Zuhair
Jan 7, 2017

We take $x-[x]$ .

Now we know for any real number x, $x= [x] +$ {x}

Hence {x} $= x - [x]$

Hence {x} is our function known as functional part,

Now we see that for any number say $1.4$ , and $2.4$ , $3.4$ , we get { $1.4$ } $=0.4$ and { $2.4$ }= $0.4$ and { $3.4$ }= $0.4$

And this is an single answer question so our only answer is $x - [x]$

i dont think this is level 4

Rohith M.Athreya - 4 years, 4 months ago