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find lim x tends to 0
sin 2x + 3x / 4x - sin 5x

\lim_{x \to 0} \frac{\sin 2 x + 3 x}{4 x - \sin 5 x} = \lim_{x \to 0} \frac{\frac{\sin 2 x}{2 x} + \frac{3 x}{2 x}}{\frac{4 x}{5 x} - \frac{\sin 5 x}{5 x}} \times (\frac{2 x}{5 x}) = \frac{2}{5} \frac{\lim_{x \to 0} (\frac{\sin 2 x}{2 x} + \frac{3}{2})}{\lim_{x \to 0} (\frac{4}{5} - \frac{\sin 5 x}{5 x})} = \frac{2}{5} \times \frac{(1 + \frac{3}{2})}{(\frac{4}{5} - 1)} = \frac{2}{5} \times \frac{- 1}{2} = \frac{- 1}{5}

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