Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 30

Find the infinite limit for $\lim\limits_{x \rightarrow \pi^-} \cot x $


$
\begin{array}{|c|c|}
\hline
x & f(x)\\
\hline
\pi - 0.1 & -9.9666\\
\pi - 0.01 & -99.9966\\
\pi - 0.001 & -999.9996\\
\pi - 0.0001 & -9999.9999\\
\hline
\end{array}
$


According to the table, as the values of $x$ approaches $\pi$ from the left side, the values of the limit approaches $-\infty$


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \to \pi^-} \cot x & = \lim\limits_{x \to \pi^-} \displaystyle \frac{1}{\tan x} = \frac{1}{\tan (\pi - 0.0001)}\\
\lim\limits_{x \to \pi^-} \cot x & = -9999.999
\end{aligned}
\end{equation}
$