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lim(x to 1)(log ex)^(1//logx) is equal t...

`lim_(x to 1)(log ex)^(1//logx)` is equal to

A

` e^(-1)`

B

`e`

C

`e^(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_(x to 1)""(log ex)^(1//log x)=lim_(x to 1)[log e+ log x]^(1//log x)`
`= lim_( x to oo)[1+log x]^(1//log x)`
`=e^(lim_(x to 1)""(log x )/( log x ))=e `
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