Evaluate $\lim_{x\to0}\frac{1-\cos3x+\sin 3x}x$ without L'Hôpital's rule I've been trying to solve this question for hours. It asks to find the limit without L'Hôpital's rule.
$$\lim_{x\to0}\frac{1-\cos3x+\sin3x}x$$
Any tips or help would be much appreciated.

Here is a similar approach also relying on the standard table limit $\lim\limits_{x\to 0}\frac{\sin x}{x}=1$:
$\lim\limits_{x\to 0}\frac{1-\cos(3x)+\sin(3x)}{x}=\lim\limits_{x\to 0}\frac{\frac{(1+\sin(3x))^2-\cos^2(3x)}{x}}{1+\sin(3x)+\cos(3x)}=\lim\limits_{x\to 0}\frac{2\cdot\frac{\sin (3x)}{x}(1+\sin(3x))}{1+\sin(3x)+\cos(3x)}=3$
