limit as x approaches-2+of (x-1)/(x^2-4)

解

x \to - 2 + lim (\frac{x - 1}{x ^{2} - 4})

\infty

解答ステップ

x \to - 2 + lim (\frac{x - 1}{x ^{2} - 4})

\frac{x - 1}{x ^{2} - 4} = (x - 1) \frac{1}{x ^{2} - 4}

= x \to - 2 + lim ((x - 1) \frac{1}{x ^{2} - 4})

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 (x - 1) \cdot x \to - 2 + lim (\frac{1}{x ^{2} - 4})

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

x \to - 2 + lim (\frac{1}{x ^{2} - 4}) = - \infty

= (- 3) (- \infty)

無限大の特性を適用する:

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

= \infty