[Tex]\lim_{x\to 0}\dfrac{\tan(2x)-x}{3x-\sin(x)}[/Tex]

[Tex]\text{Find the values of } a \text{ and } b \text{ such that } f(x)= \begin{cases} x+a\sqrt{2}\sin x, & 0\leq x<\frac{\pi}{4} \\[6pt] 2x\cot x+b, & \frac{\pi}{4}\leq x\leq \frac{\pi}{2} \\[6pt] a\cos 2x-b\sin x, & \frac{\pi}{2}<x\leq \pi \end{cases}[/Tex]