_ x 0 x^x = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} {x^x} = $

A
$0$
✓
$1$
C
$e$
D
None of these

✓

Answer

Correct option: B.

$1$

b
(b) Let $y = {x^x}\, \Rightarrow \,\,\,\log y = x\log x$

$\therefore \,\,\mathop {\lim }\limits_{y \to 0} \,\log y = \mathop {\lim }\limits_{x \to 0} x\log x$

$ = 0 = \log 1\,\, \Rightarrow \,\,\mathop {\lim }\limits_{x \to 0} {x^x} = 1$.

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