Question

Find the limit as x is approaching 0 of cot(3x)sin(6x)

Please tell me where I am going wrong in my work, which I will post below in the comments.

Answer 1

`\lim_(x \to 0) \cot (3x) \sin (6x) = \lim_(x \to 0) (\cos(3x))/(\sin(3x)) \cdot \sin(6x) = \\ \\ = \lim_(x \to 0) (\cos(3x))/(\sin(3x)) \cdot 2 \sin (3x) \cdot \cos(3x) = \lim_(x \to 0) 2 \cos^(2) (3x) = \\ \\ = 2 \cdot 0 = \boxed{2}`