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lim(xto-1) (1)/(sqrt(|x|-{-x})) (where {...

`lim_(xto-1) (1)/(sqrt(|x|-{-x}))` (where `{x}` denotes the fractional part of x) is equal to

A

16

B

24

C

32

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
L.H.L.`=underset(xto-1^(-))lim(1)/(sqrt(|x|-{-x}))=underset(xto-1^(-))lim(1)/(sqrt(-x-(x+2)))`
`=underset(xto-1^(-))lim(1)/(sqrt(-2x-2))=oo`
R.H.L.`=underset(xto-1^(+))lim(1)/(sqrt(|x|-{-x}))=underset(xto-1^(-))lim(1)/(sqrt(-x-(x+1)))`
`=underset(xto-1^(-))lim(1)/(sqrt(-2x-1))=1`
Hence, the limit does not exist.
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