$\lim\limits_{x \to 0} f(x) = \dfrac{\sin2x}{x\cos3x}$
By the product law, can't we write:
$= 2 \cdot \lim\limits_{x \to 0} \dfrac{\sin2x}{2x} \cdot \lim\limits_{x \to 0} \dfrac{1}{\cos3x}$
Then taking the limits, replace $2x$ with $\theta$ and $\theta$ approaches $0$ if you like
$= 2 \cdot 1 \cdot \dfrac{1}{1}$
$= 2$ ?
However wolfram says it is $-\infty$ on one side and $+\infty$ on the other, and I am inclined to believe it :)
Where am I messing up?