Let [x] denotes the greatest integer less than or equal to x. If `f(x) = [x sin pix]`, then f(x) is

Options

A. continuous at x = 0
B. continuous in (-1, 0)
C. differentiable in (-1,1)
D. All of these

Answer

C

Explanation

Here, when
`-1lexle1,0lex sin pi x lt1`
`impliesf(x)=[xsinpix]=0" for "-1lexle1`
i.e. f(x) is constant function (equal to zero) in [-1, 1].
`implies` f(x) is differentiable in (-1, 1).