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# Let $g(x) = \text{sgn}(\sin x)$.(a) Find each of the following limits or explain why it does not exist. (i) $\displaystyle \lim_{x \to 0^+}g(x)$ (ii) $\displaystyle \lim_{x \to 0^-}g(x)$ (iii) $\displaystyle \lim_{x \to 0}g(x)$ (iv) $\displaystyle \lim_{x \to \pi^+}g(x)$ (v) $\displaystyle \lim_{x \to \pi^-}g(x)$ (vi) $\displaystyle \lim_{x \to \pi}g(x)$(b) For which values of $a$ does $\displaystyle \lim_{x \to a}g(x)$ not exist?(c) Sketch a graph of $g$.

## a. $\begin{array}{llllll}{\text { (i) } 1} & {\text { (ii) }-1} & {\text { (iii) DNE }} & {\text { (iv) }-1} & {\text { (v) } 1} & {\text { (vi) DNE }}\end{array}$b. $\lim _{x \rightarrow a} \operatorname{sgn}(\sin x)$ will not exist if $a=n \pi$c. Answer not available

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