[tex] \lim_{x \to 0} \cot{2x}\sin{6x}
\\
\\\lim_{x \to 0} \frac{\cos{2x}\sin{6x}}{\sin{2x}}
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\\\lim_{x \to 0} \frac{(\cos{2x}\sin{6x})'}{(\sin{2x})'}
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\\ \lim_{x \to 0} \frac{-2\sin{2x} \sin{6x}+6\cos{6x} \cos{2x}}{2\cos{2x}}
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\\ \frac{-2\sin{0} \sin{0}+6\cos{0} \cos{0}}{2\cos{0}}
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\\\frac{-2\times 0+6\times1\times1}{2\times1}
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\\ \frac{6}{2}
\\
\\3[/tex]
