問題：次の式を計算せよ

• (1) \( \displaystyle \lim_{x \to 0} \dfrac{\sin 3x}{x} \)


• (2) \( \displaystyle \lim_{x \to \infty} x\tan \dfrac{1}{x} \)


• (3) \( \displaystyle \lim_{h \to 0} \dfrac{2\cos(x+\frac{h}{2})\sin\frac{h}{2}}{h} \)


• (4) \( \displaystyle \lim_{x \to 0} \dfrac{\sin x^\circ}{x} \)


• (5) \( \displaystyle \lim_{x \to \infty} \dfrac{2x - \cos x}{x + \cos x} \)