To match the resulting values to the corresponding limits, we need to pair the given limits with the correct calculated values. Here are the matches based on the provided results:
1. [tex]$
\lim _{x \rightarrow 8}\left(\frac{8-x}{\left|-x^2-63 x+568\right|}\right)
$[/tex] matches with [tex]$-\frac{1}{79}$[/tex].
2. [tex]$
\lim _{x \rightarrow 6^{-}}\left(\frac{|x-6|}{-x^2-86 x+852}\right)
$[/tex] matches with [tex]$0$[/tex].
3. [tex]$
\lim _{x \rightarrow 7^{+}}\left(\frac{-x^2-178+168}{|x-5|}\right)
$[/tex] matches with [tex]$-29.5$[/tex].
So, the correct pairs are:
- [tex]$\lim _{x \rightarrow 8}\left(\frac{8-x}{\left|-x^2-63 x+568\right|}\right)$[/tex]: [tex]$-\frac{1}{79}$[/tex]
- [tex]$\lim _{x \rightarrow 6^{-}}\left(\frac{|x-6|}{-x^2-86 x+852}\right)$[/tex]: [tex]$0$[/tex]
- [tex]$\lim _{x \rightarrow 7^{+}}\left(\frac{-x^2-178+168}{\left|x-5 \right|}\right)$[/tex]: [tex]$-29.5$[/tex]
