limit as x approaches-9+of (x+8)/(x+9)

解

x \to - 9 + lim (\frac{x + 8}{x + 9})

- \infty

解答ステップ

x \to - 9 + lim (\frac{x + 8}{x + 9})

\frac{x + 8}{x + 9} = (x + 8) \frac{1}{x + 9}

= x \to - 9 + lim ((x + 8) \frac{1}{x + 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 - 9 + lim (x + 8) \cdot x \to - 9 + lim (\frac{1}{x + 9})

x \to - 9 + lim (x + 8) = - 1

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

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty