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If f(x)={{:((e^(|x|+2x+1)-1)/([2x]+2x+1)...

If `f(x)={{:((e^(|x|+2x+1)-1)/([2x]+2x+1),":",xne0),(1,":",x=0):}` then (where `[.]` represents the greatest integer function)

A

`lim_(xrarr0^(+))f(x)=1`

B

`lim_(xrarr0^(-))f(x)=e-1`

C

`f(x)` is continuous at x = 0

D

`f(x)` is discontinuous at x = 0

Text Solution

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The correct Answer is:
D
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