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If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) the...

If `f(x)=x((e^(|x|+[x])-2)/(|x|+[x]))` then (where [.] represent the greatest integer function)

A

`underset(xrarr0^(+))(lim)f(x)=-1`

B

`underset(xrarr0^(-))(lim)f(x)=0`

C

`underset(xrarr0)(lim)f(0)=-1`

D

`underset(xrarr0)(lim)f(x)=0`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`underset(xrarr0^(+))(lim)x((e^(|x|+[x])-2)/(|x|+[x]))`
`=underset(xrarr0^(+))(lim)x((e^(x+0)-2)/(x+0))`
`=underset(xrarr0^(+))(lim)(e^(x)-2)`
`=1-2=-1`
`underset(xrarr0^(-))(lim)x((e|x|+[x]-2)/(|x|+[x]))`
`=underset(xrarr0^(-))(lim)x((e^(-x-1)-2)/(-x-1))=0`
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