lim(xto0) [(sin(sgn(x)))/((sgn(x)))], wh...

`lim_(xto0) [(sin(sgn(x)))/((sgn(x)))],` where `[.]` denotes the greatest integer function, is equal to

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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