13. $lim_{x\rightarrowpi^{+}}cot x$

Explanation:

Step1: Recall cotangent definition

$\cot x=\frac{\cos x}{\sin x}$

Step2: Analyze $\cos x$ and $\sin x$ as $x\to\pi^{+}$

As $x\to\pi^{+}$, $\cos x\to - 1$ and $\sin x\to0^{-}$ (since $\sin x$ is negative for $x$ slightly greater than $\pi$).

Step3: Determine the limit

$\lim_{x\to\pi^{+}}\cot x=\lim_{x\to\pi^{+}}\frac{\cos x}{\sin x}=\frac{-1}{0^{-}}=+\infty$

Answer:

$+\infty$