limit as x approaches-3+of (x+2)/(x^2-9)

解

x \to - 3 + lim (\frac{x + 2}{x ^{2} - 9})

\infty

解答ステップ

x \to - 3 + lim (\frac{x + 2}{x ^{2} - 9})

\frac{x + 2}{x ^{2} - 9} = (x + 2) \frac{1}{x ^{2} - 9}

= x \to - 3 + lim ((x + 2) \frac{1}{x ^{2} - 9})

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 - 3 + lim (x + 2) \cdot x \to - 3 + lim (\frac{1}{x ^{2} - 9})

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

x \to - 3 + lim (\frac{1}{x ^{2} - 9}) = - \infty

= (- 1) (- \infty)

無限大の特性を適用する:

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

= \infty