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lim(x rarr0)(tanx)^(1/x)...

`lim_(x rarr0)(tanx)^(1/x)`

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Evaluate : lim_(x rarr 0)(tanx/x)^(1/x)

lim_(x rarr0)(1-x)^(1/x)=

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L_(1)=lim_(x rarr0^+)(1+x)^(1/x),L_(2)=lim_(x rarr0^(+))(1+x)^(1/x^(2)),L_(3)=lim_(x rarr0^(+))(1+x^(2))^(1/x) ,Then

lim_(x rarr0)(1+x)^((1)/(x))=e

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