由和差化积公式得：  $$\sin 2x+\sin 4x=2\cos x\sin 3x$$，  ∴原式$$=\left\textbar{} 2\cos x\sin 3x+\sin 3x \right\textbar$$$$=\left\textbar{} 2\cos +1 \right\textbar\cdot \left\textbar{} \sin 3x \right\textbar$$，  又$$\left\textbar{} 2\cos x+1 \right\textbar$$最小正周期为$$2\pi $$，  $$\left\textbar{} \sin 3x \right\textbar$$最小正周期为$$\frac{\pi }{3}$$，  故$$f\left( x \right)$$最小正周期为$$2\pi $$． 
函数$$f\left( x \right)=\left\textbar{} \sin 2x+\sin 3x+\sin 4x \right\textbar$$的最小正周期为~\uline{~~~~~~~~~~}~．
  - $$\pi$$ 
  - $$2\pi$$ 
  - $$3\pi$$ 
  - $$4\pi$$ 