breachaOse breachaOse

26-11-2016
Mathematics

Answered

lim Cot(2x) Sin(6x) (l'hospital's rule section)

x -> 0

Verified Answer :

alsteva alsteva

29-11-2016

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

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