正弦的重要极限

求下列极限。所有角均以弧度为单位。

(a) $\displaystyle \lim\limits_{t\to0}\dfrac{5\sin(t)}{2t}$

(b) $\displaystyle \lim\limits_{\theta\to0}\dfrac{\theta}{\sin(4\theta)}$

(c) $\displaystyle \lim\limits_{x\to-1}\dfrac{\sin^2(x+1)}{(x+1)^2}$

(d) $\displaystyle \lim\limits_{x\to0}\dfrac{\sin(3x)}{\sin(2x)}$

(e) $\displaystyle \lim\limits_{\theta\to0}\dfrac{100\theta}{\tan(3\theta)}$

(f) $\displaystyle \lim\limits_{h\to0}\dfrac{\cos(h)-1}{h}$