Question

Evaluate : `Lim_(x→0) (x)^(1/(1-x))`

Answer 1

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`