Answer
$\lim\limits_{x\to\frac{5\pi}{6}}\sin{x}=\dfrac{1}{2}.$
Work Step by Step
Using Theorem $1.6:$
$\lim\limits_{x\to\frac{5\pi}{6}}\sin{x}=\sin{\frac{5\pi}{6}}=\dfrac{1}{2}.$
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