In Exercises 31 and $32,$ sketch the graph of $f$ . Then identify the values of $c$ for which $$\lim _{x \rightarrow e} f(x)$$

$$f(x)=\left\{\begin{array}{ll}{\sin x,} & {x < 0} \\ {1-\cos x,} & {0 \leq x<\pi} \\ {\cos x,} & {x>\pi}\end{array}\right.$$

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## Recommended Questions

Prove the limit statements in Exercises 37-50.

$$\lim _{x \rightarrow 1} f(x)=2 \quad \text { if } \quad f(x)=\left\{\begin{array}{ll}{4-2 x,} & {x<1} \\ {6 x-4,} & {x \geq 1}\end{array}\right.$$

$\begin{array}{l}{\text { Determining Differentiability In Exercises }} \\ {77-80, \text { describe the } x \text { -values at which } f \text { is }} \\ {\text { differentiable. }}\end{array}$

$$f(x)=\left\{\begin{array}{ll}{x^{2}-4,} & {x \leq 0} \\ {4-x^{2},} & {x>0}\end{array}\right.$$