("lim")(xvec0)[(sin(sgn(x)))/((sgn(x)))]...

`("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))],` where`[dot]` denotes the greatest integer function, is equal to (a)0 (b) 1 (c) `-1` (d) does not exist

A

`^(2n)p_(n)`

B

`^(2n)C_(n)`

C

`(2n)!`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A

`underset(xto0^(+))lim[(sin(sgnx))/(sgn(x))]=underset(xto0^(+))lim[(sin1)/(1)]=0`
`underset(xto0^(-))lim[(sin(sgnx))/(sgn(x))]`
`=underset(xto0^(-))lim[sin(-1)/(-1)]`
`=underset(xto0^(-))lim[sin1]`
Hence, the given limit is 0.

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Knowledge Check

int_(0)^(1)[2x]dx where [] is the greatest integer function :

A

1

B

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C

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D

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