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Value of limit lim(xrarr0^(+))x^(x^(x))....

Value of limit `lim_(xrarr0^(+))x^(x^(x)).ln(x)` is

A

`1`

B

`0`

C

Does not exists

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
B
`"lt"_(xrarr0^(+)) x^(x^(x)).ln(x)="lt"_(xrarr0^(+)).xln(x)`
`="lt"_(xrarr0^(+))xln(x).exp.(ln(x^(x^(x)-1))`
`"lt"_(xrarr0^(+))xln(x).exp.((x^(x)-1)ln(x))`
`="lt"_(xrarr^(0^(+))xln(x).exp((e^(xIn(x))-1).ln(x))`
`"lt"_(xrarr0^(+))xln(x).exp.(((e^(xIn(x))-1)/(xIn(x))).xln^(2)(x))`
`ouarr.xp(1.0uarr)`
`ouarr.1=0`
(using `"lt"_(xrarr0^(+))x^(m).In(x)=0` for `mgt0`)
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