If G(x) = - 25 - x^2 , then _ x 1 G(x) - G(1) x - 1 = - Vidyadip

MCQ

If $G(x) = - \sqrt {25 - {x^2}} $, then $\mathop {\lim }\limits_{x \to 1} \frac{{G(x) - G(1)}}{{x - 1}} = $

A
$\frac{1}{{24}}$
B
$\frac{1}{5}$
C
$ - \sqrt {24} $
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) $\mathop {\lim }\limits_{x \to 1} \,\,\frac{{G(x) - G(1)}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \,\,\frac{{ - \sqrt {25 - {x^2}} + \sqrt {24} }}{{x - 1}}$
{Multiply both numerator and denominator by $(\sqrt {24} + \sqrt {25 - {x^2}} )$}
$ = \mathop {\lim }\limits_{x \to 1} \,\,\frac{{x + 1}}{{\sqrt {24} + \sqrt {25 - {x^2}} }} = \frac{1}{{\sqrt {24} }}$ .

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