Question

Lim Cot(2x) Sin(6x) (l'hospital's rule section)
x -> 0

Answer 1

`\lim_(x \to 0) \cot{2x}sin(6x) \\ \\\lim_(x \to 0) (cos(2x)sin(6x))/(sin(2x)) \\ \\\lim_(x \to 0) ((cos(2x)sin(6x))')/((sin(2x))') \\ \\ \lim_(x \to 0) (-2sin(2x) sin(6x)+6cos(6x) cos(2x))/(2cos(2x)) \\ \\ (-2sin(0) sin(0)+6cos(0) cos(0))/(2cos(0)) \\ \\(-2* 0+6*1*1)/(2*1) \\ \\ (6)/(2) \\ \\3`