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Evaluate : Lim X → 0 ( X ) 1 1 − X - Applied Mathematics 1

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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