不定形の極限値(limit of indeterminate forms)

演習問題

1.: 次の極限値を求めよう．
(a): $\displaystyle{\lim_{x \rightarrow 0}\frac{\sin{2x}}{\sin{3x}}}$
(b): $\displaystyle{\lim_{x \rightarrow 0}\frac{\cos{x} - 1}{x}}$
(c): $\displaystyle{\lim_{x \rightarrow 0}\frac{\sin^{-1}{x}}{x}}$
(d): $\displaystyle{\lim_{x \rightarrow 0}x\sin{\frac{1}{x}}}$
(e): $\displaystyle{\lim_{x \rightarrow 0}(\frac{1}{x^{2}} - \frac{1}{\sin^{2}{x}})}$
(f): $\displaystyle{\lim_{x \rightarrow \frac{\pi}{2}}(1 - \sin{x})^{\cos{x}}}$
(g): $\displaystyle{\lim_{x \rightarrow 0}(\frac{e^{x} - 1}{x})^{1/x}}$
(h): $\displaystyle{\lim_{x \rightarrow 0}(1 - x)^{\frac{1}{\sin{x}}}}$