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Question

limxelnx1|xe| is equal to

A
1/e
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B
1/e
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C
e
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D
does not exist
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Solution

The correct option is D does not exist
Let, L=limxelnx1|xe|.
Now the right hand limit i.e.
RHL =limxe+lnx1xe 00 form
Now L'Hospital's rule we get,
or, RHL =limxe+1x1=1e.......(1).
Again, the right hand limit i.e.
LHL =limxelnx1x+e 00 form
Now L'Hospital's rule we get,
or, LHL =limxe1x1=1e.......(2).
Since RHLLHL, so the given limit doesn't exit.

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