Solve for: \lim_{x arrow-1} ((5x+1)/(x+1))

Expression: $\lim_{x \rightarrow -1} \left(\frac{ 5x+1 }{ x+1 }\right)$

Since the function $\frac{ 5x+1 }{ x+1 }$ is undefined for $-1$, evaluate the left-hand and right-hand limits

$\begin{array} { l }\lim_{x \rightarrow -1^-} \left(\frac{ 5x+1 }{ x+1 }\right),\\\lim_{x \rightarrow -1^+} \left(\frac{ 5x+1 }{ x+1 }\right)\end{array}$

Evaluate the limit

$\begin{array} { l }+\infty,\\\lim_{x \rightarrow -1^+} \left(\frac{ 5x+1 }{ x+1 }\right)\end{array}$

Evaluate the limit

$\begin{array} { l }+\infty,\\-\infty\end{array}$

Since the left-hand and the right-hand limits are different, the limit $\lim_{x \rightarrow -1} \left(\frac{ 5x+1 }{ x+1 }\right)$ does not exist

$\textnormal{Does not exist}$