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

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