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lim(xrarrc)f(x) does not exist for whe...

`lim_(xrarrc)f(x)` does not exist for
wher `[.]` represent greatest integer function `{.}` represent fractional part function

A

`f(x)=[x]-x,c=0`

B

`f(x)=[|x|]-[2x-1],c=3`

C

`f(x)={x}^(2)-{-x}^(2),c=0`

D

`f(x)=(tan(sgn x))/((sgn x)),c=0`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
(A) `lim_(xrarr3)[|x|]-[2x-1]`
R.H.L `x=3-impliesf(3^(+))=3-5=-2`
L.H.L `x=3^(-)impliesf^(3^(-))=2-4=-2`
(B) `f(0^(+))=0-0=0,f(0^(-))=-1`
(C) `f(x)=(x-[x])^(2)-(-x-[-x])^(2)`
`f(0^(+))=0-(+1)^(2)=-1`
`f(0^(-))=(0-1)-(0-0)^(2)=1`
(D) `f(0^(+))=(tan1)/1=tan1`
`f(0^(-))=(tan(-1))/(-1)=tan1`
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