右側極限値，左側極限値(right-hand limit, left-hand limit)

演習問題

1.: 次の関数の極限値を求めよう．
(a): $\displaystyle{\lim_{x \rightarrow 0}\frac{1}{x}}$
(b): $\displaystyle{\lim_{x \rightarrow 0}\frac{1}{x^{2}}}$
(c): $\displaystyle{\lim_{x \rightarrow 0+}\frac{\vert x\vert}{\sqrt{a+x} - \sqrt{a-x}}}$
(d): $\displaystyle{\lim_{x \rightarrow 0-}\frac{x}{\sqrt{1-\cos{x}}}}$
(e): $\displaystyle{\lim_{x \rightarrow \infty}\cos{\frac{1}{x}}}$
(f): $\displaystyle{\lim_{x \rightarrow \infty}\frac{\sin{x}}{x}}$
(g): $\displaystyle{\lim_{x \rightarrow 0+}\cos{\frac{1}{x}}}$