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