Lim_x → 1 x^(11 x^2) =e^lim_x → 1 (x 1)(11 x^2) =e^lim_x → 1 (x 1)(1(1 x)(1+x)) nbsp; =e^ 1/2 ...

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Binomial Expression

limx → 1 x11-...

Question

$lim x \to 1 x^{⎛ ⎝ \frac{1}{1 - x^{2}} ⎞ ⎠} =$

e^{\frac{1}{2}}

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e^{\frac{- 1}{2}}

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e^{\frac{1}{3}}

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e

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Solution

The correct option is B $e^{\frac{- 1}{2}}$
$lim x \to 1 x^{⎛ ⎝ \frac{1}{1 - x^{2}} ⎞ ⎠}$
$= e^{lim x \to 1 (x - 1) (\frac{1}{1 - x^{2}})}$
$= e^{lim x \to 1 (x - 1) (\frac{1}{(1 - x) (1 + x)})}$
$= e^{- 1 / 2}$

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