If \({\rm{F}}\left( {\rm{x}} \right) = \sqrt {9 - {{\rm{x}}^2}} \), then what is \(\mathop {\lim }\limits_{{\rm{x}} \to 1} \frac{{{\rm{F}}\left( {\rm{x}} \right) - {\rm{F}}\left( 1 \right)}}{{{\rm{x}} - 1}}\) equal to?
1
\( - \frac{1}{{4\sqrt 2 }}\)
2
\(\frac{1}{8}\)
3
\(- \frac{1}{{2\sqrt 2 }}\)
4
\(\frac{1}{{2\sqrt 2 }}\)