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For a real number x let [x] denote the l...

For a real number x let [x] denote the largest number less than or equal to x. For ` x in R` let f (x)=[x] `sin pix`. Then

A

If is differentiable on R.

B

f is symmetric about the line x=0

C

`int_(-3)^(3)f(x)dx=0`

D

For each real `alpha`, the equation `f(x) -alpha =0` has infinitely many roots.

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The correct Answer is:
D
`f(x) =[x] sin pix`

Not diff for `AAx in R`
Not sym about x=0
`overset(3)underset(-3)intf (x)dxne0`
`f(x) =alpha` will be `oo` sol"
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