_ x a (x + 2) ^ 5/3 - (a + 2) ^ 5/3 x - a = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to a} \frac{{{{(x + 2)}^{5/3}} - {{(a + 2)}^{5/3}}}}{{x - a}} = $

✓
$\frac{5}{3}{(a + 2)^{2/3}}$
B
$\frac{5}{3}{(a + 2)^{5/3}}$
C
$\frac{5}{3}{a^{2/3}}$
D
$\frac{5}{3}{a^{5/3}}$

✓

Answer

Correct option: A.

$\frac{5}{3}{(a + 2)^{2/3}}$

a
(a) Apply the $L-$ Hospital‘s rule,

$\mathop {\lim }\limits_{x \to a} \frac{{f(x)}}{{g(x)}} = \mathop {\lim }\limits_{x \to a} \frac{{f'(x)}}{{g'(x)}}$.

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