limit as h approaches 1-of (h-2)/(1-h)

解

h \to 1 - lim (\frac{h - 2}{1 - h})

- \infty

解答ステップ

h \to 1 - lim (\frac{h - 2}{1 - h})

\frac{h - 2}{1 - h} = (h - 2) \frac{1}{1 - h}

= h \to 1 - lim ((h - 2) \frac{1}{1 - h})

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

= h \to 1 - lim (h - 2) \cdot h \to 1 - lim (\frac{1}{1 - h})

h \to 1 - lim (h - 2) = - 1

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

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty