Limit of indeterminate forms

Exercise

1.

Find the follosing limit．

(a)

$${\lim_{x \rightarrow 0}\frac{\sin{2x}}{\sin{3x}}}$$

(b)

$${\lim_{x \rightarrow 0}\frac{\cos{x} - 1}{x}}$$

(c)

$${\lim_{x \rightarrow 0}\frac{\sin^{-1}{x}}{x}}$$

(d)

$${\lim_{x \rightarrow 0}x\sin{\frac{1}{x}}}$$

(e)

$${\lim_{x \rightarrow 0}(\frac{1}{x^{2}} - \frac{1}{\sin^{2}{x}})}$$

(f)

$${\lim_{x \rightarrow \frac{\pi}{2}}(1 - \sin{x})^{\cos{x}}}$$

(g)

$${\lim_{x \rightarrow 0}(\frac{e^{x} - 1}{x})^{1/x}}$$

(h)

$${\lim_{x \rightarrow 0}(1 - x)^{\frac{1}{\sin{x}}}}$$