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Number of points of non-differerentiable...

Number of points of non-differerentiable of `f(x)=sin pi(x-[x])"in "(-pi//2,[pi//2).` Where [.] denotes the greatest integer function is

A

f(x) is discontinuous at `x = {-1, 0, 1}`

B

f(x) is differentiable for `x in (-(pi)/(2),(pi)/(2))-{0}`

C

f(x) is differentiable for `x in (-(pi)/(2),(pi)/(2)) - {-1, 0, 1}`

D

None of these

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • Number of points of non-differentiability of f(x)=sin pi(x-[x]) in (-pi//2,pi//2) , where [.] denotes greatest integer function is

    A
    4
    B
    5
    C
    3
    D
    2

  • Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

    A
    continuous at integer points
    B
    continuous everywhere
    C
    differentiable once but f''(x) and f''' (x) do not exist
    D
    differentiable for all x

  • Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the greatest integer function then f(x) is

    A
    continuous and differentiable at all ` x in R `
    B
    continuous but not differentiable at some x
    C
    Differentiable but not continuous at x =0
    D
    Neither continuous nor differentiable at x =0

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