# Chapter 4 - Review - Exercises - Page 359: 12

$\lim\limits_{x \to \pi^-}(x-\pi)~csc~x = -1$

#### Work Step by Step

$\lim\limits_{x \to \pi^-}(x-\pi)~csc~x = \lim\limits_{x \to \pi^-}\frac{x-\pi}{sin~x}= \frac{0}{0}$ We can use L'Hospital's Rule: $\lim\limits_{x \to \pi^-}\frac{x-\pi}{sin~x}$ $=\lim\limits_{x \to \pi^-}\frac{1}{cos~x}$ $=\frac{1}{-1}$ $= -1$

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