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

解

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

- \infty

解答ステップ

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

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

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

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

x \to - 1 + lim (x - 2) = - 3

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

= (- 3) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty