limit as x approaches-2-of (x-3)/(x^2-4)

解

x \to - 2 - lim (\frac{x - 3}{x ^{2} - 4})

- \infty

解答ステップ

x \to - 2 - lim (\frac{x - 3}{x ^{2} - 4})

\frac{x - 3}{x ^{2} - 4} = (x - 3) \frac{1}{x ^{2} - 4}

= x \to - 2 - lim ((x - 3) \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 - 3) \cdot x \to - 2 - lim (\frac{1}{x ^{2} - 4})

x \to - 2 - lim (x - 3) = - 5

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

= (- 5) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty