limit as x approaches 2+of (1-x)/(x-2)

解

x \to 2 + lim (\frac{1 - x}{x - 2})

- \infty

解答ステップ

x \to 2 + lim (\frac{1 - x}{x - 2})

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

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

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 2 + lim (1 - x) \cdot x \to 2 + lim (\frac{1}{x - 2})

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

x \to 2 + lim (\frac{1}{x - 2}) = \infty

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty