## Calculus 8th Edition

$-\infty$
$\displaystyle \cot x=\frac{\cos x}{\sin t}$ 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. $\displaystyle \lim_{x\rightarrow\pi^{-}}\cot x=-\infty$