If G(x)=−25−x then limx→1 G(x)−G(1)x−1 has the value

If $G (x) = - \sqrt{25 - x}$ then $lim_{x \to 1} \frac{G (x) - G (1)}{x - 1}$ has the value

A
$\frac{1}{\sqrt{2.4}}$
B
$\frac{1}{5}$
C
$- \sqrt{24}$
D
$- 1 / 5$

Solution:

We have,

$lim_{x \to 1} \frac{G (x) - G (1)}{x - 1} = G^{'} (1)$ [By def. of derivative]

Now,

$G (x) = - \sqrt{25 - x^{2}} \Rightarrow G^{'} (x) = \frac{x}{\sqrt{25 - x^{2}}} \Rightarrow G^{'} (1) = \frac{1}{\sqrt{24}}$

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