Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the resulting values to the corresponding limits.

[tex]\[
\lim _{x \rightarrow 8}\left(\frac{8-x}{|-x^2-63x+568|}\right)
\][/tex]
[tex]$\square$[/tex]

[tex]\[
\lim _{x \rightarrow 6^{-}}\left(\frac{|x-6|}{-x^2-86x+852}\right)
\][/tex]
[tex]$\square$[/tex]

[tex]\[
\lim _{x \rightarrow 7^{+}}\left(\frac{-x^2-178+168}{|x-5|}\right)
\][/tex]
[tex]$\square$[/tex]

-31 [tex]$\square$[/tex]

[tex]$-\frac{1}{71}$[/tex] [tex]$\square$[/tex]

[tex]$\square$[/tex]



Answer :

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]