limit as x approaches-5+of (x+4)/(x+5)

解

x \to - 5 + lim (\frac{x + 4}{x + 5})

- \infty

解答ステップ

x \to - 5 + lim (\frac{x + 4}{x + 5})

\frac{x + 4}{x + 5} = (x + 4) \frac{1}{x + 5}

= x \to - 5 + lim ((x + 4) \frac{1}{x + 5})

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 - 5 + lim (x + 4) \cdot x \to - 5 + lim (\frac{1}{x + 5})

x \to - 5 + lim (x + 4) = - 1

x \to - 5 + lim (\frac{1}{x + 5}) = \infty

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty