Evaluate : `Lim_(x→0) (x)^(1/(1-x))`

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#### Solution

Let ` L= Lim_(x→0) (x)^(1/(1-x)`

Take log on both the sides,

∴ `Log L = Lim_(x→0) log x/(1-x)`

Apply L’Hospital rule ,

∴ `log L = Lim_(x→0)1/x`

=0

∴ `L=e^0=1`

Concept: Review of Complex Numbers‐Algebra of Complex Number

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