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If f(x) = {{:("sin"(pix)/(2)",",x lt 1),...

If `f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):}`, where [x] denotes the greatest integer function, then

A

f(x) is continuous at x = 1

B

f(x) is discontinuous at x = 1

C

`f(1^(+)) = 0`

D

`f(1^(-)) = -1`

Text Solution

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The correct Answer is:
A
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  • If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

    A
    is continuous at `x=(1)/(2)`
    B
    is discontinuous at `x=(1)/(2)`
    C
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    D
    `underset(x to ((1)/(2))^(-))lim f(x)=1`

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    A
    f(x) is continuous for all `x in [0, 2)`
    B
    f(x) is differentiable for all `x in [0, 2) - {1}`
    C
    f(X) is differentiable for all `x in [0, 2)-{(1)/(2),1}`
    D
    None of these

  • If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

    A
    `-1`
    B
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    C
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    D
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