To check if the limit exists,
[tex]\lim _{x\to-7}\frac{7-|x|}{7+x}[/tex]
Inputting limit,
[tex]\begin{gathered} \lim _{x\to-7}\frac{7-|(-7)|}{7+(-7)} \\ \lim _{x\to-7}\frac{7-7}{7-7}=\frac{0}{0} \end{gathered}[/tex]
Since the denominator is 0, the expression is undefined.
Therefore, the limit does not exist as x tends to -7. (DNE)
