limit as x approaches 1+of (1+x)/(1-x)

解

x \to 1 + lim (\frac{1 + x}{1 - x})

- \infty

解答ステップ

x \to 1 + lim (\frac{1 + x}{1 - x})

\frac{1 + x}{1 - x} = (1 + x) \frac{1}{1 - x}

= x \to 1 + lim ((1 + x) \frac{1}{1 - x})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

不定形式の場合を除く

= x \to 1 + lim (1 + x) \cdot x \to 1 + lim (\frac{1}{1 - x})

x \to 1 + lim (1 + x) = 2

x \to 1 + lim (\frac{1}{1 - x}) = - \infty

= 2 (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty