can someone verify that the limit does not exist? i got -1 from the left and 1 from the right. the limit is to negative 6. i used the math text tool but the negative sign isn't showing up on my screen.

Just as a tip: the source says you typed it in as\lim_{x \to \-6}, which results in  the \- is a command. backslashes are used to denote commands in latex, which is what this site's math tool is based off of. if you put a backslash in front of the hyphen, the tex compiler will not recognize it as a negative. so enter it simply as  \lim_{x \to -6}, which results in  .if you want it under, use the command \displaystyle in front. the limit in front right now is considered "textstyle," or "inline math."\lim_{x \to -6} results in  \displaystyle\lim_{x \to -6} results in  using \displaystyle also makes fractions look less compact, making them slightly easier to read. (however, this does make it look too big for use in paragraphs, so i usually use these on separate "paragraphs.")\frac{\sqrt{x^2 + 12x+36}}{x+6} results in  \displaystyle\frac{\sqrt{x^2 + 12x+36}}{x+6} results in  or use \dfrac{}{} for display fractions. this does not need \displaystyle: \dfrac{\sqrt{x^2 + 12x+36}}{x+6} results in  yes, the limit does not exist. graphical evidence is shown below. algebraic evidence: for left side, we have (typed as \displaystyle\lim_{x \to -6^-})for right side, we have (typed as \displaystyle\lim_{x \to -6^+})so yes, does not exist