_ x 1 1 - x^ - 1/3 1 - x^ - 2/3 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 1} \frac{{1 - {x^{ - 1/3}}}}{{1 - {x^{ - 2/3}}}} = $

A
$\frac{1}{3}$
✓
$\frac{1}{2}$
C
$\frac{2}{3}$
D
$ - \frac{2}{3}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

b
(b) $\mathop {\lim }\limits_{x \to 1} \,\frac{{1 - {x^{ - 1/3}}}}{{(1 - {x^{ - 1/3}})\,\,(1 + {x^{ - 1/3}})}} = \frac{1}{2}.$

Aliter : Apply $L-$ Hospital’s rule.

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