Q75 / 150 · MHT CET 2011 · Mathematics

If $G(x)=-\sqrt{25-x^{2}}$, then $\lim _{x \rightarrow 1} \frac{G(x)-G(t)}{x-1}$ is

  • A
    $\frac{1}{24}$
  • B
    $\frac{1}{5}$
  • C
    $-\sqrt{24}$
  • Correct answer
    D
    None of these

Solution

$\lim _{x \rightarrow 1} \frac{G(x)-G(1)}{x-1}=\lim _{x \rightarrow 1} G^{\prime}(x)$ $$ \begin{array}{l} =\lim _{x \rightarrow 1}-\frac{1}{2 \sqrt{25-x^{2}}}(-2 x) \\ =\frac{1}{\sqrt{24}} \end{array} $$

Hence, the correct answer is option: 'D'.

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