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lim(xto0) e^(-1//x) is equal to...

`lim_(xto0) e^(-1//x)` is equal to

A

0

B

`oo`

C

e

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
`LHL=underset(hto0^(-))lime^((-1)/((0-h)))=underset(hto0)lim^(e^((1)/(h)))`
`=e^(oo)=oo`
`RHL=underset(hto0^(+))lime^((-1)/((0+h)))=underset(hto0)lim^(e(-1)/(h))=e^(-oo)=0`
`:.LHL""neRHL`
So, `underset(xto0)lime^((-1)/(x))`
does not exist.
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