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[tex] \displaystyle \lim _{x \to - \frac{\pi}{6} }tg2x = tg(\lim _{x \to - \frac{\pi}{6}}2x) = tg( - \frac{\pi}{6} \times 2) = tg( - \frac{\pi}{3} ) = \bf - \sqrt{3} .[/tex]