Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises - Page 61: 36

$-\infty$

$\displaystyle \cot x=\frac{\cos x}{\sin t}$ With the unit circle in mind, as $x\rightarrow\pi^{-}$, it is in quadrant II, approaching $\pi.$ In quadrant II, sine is positive, cosine is negative. The numerator is negative, approaching $-1$. The denominator approaches 0, and is positive. $\displaystyle \lim_{x\rightarrow\pi^{-}}\cot x=-\infty$