limit as x approaches-5-of (3x+8)/(x+5)

解

x \to - 5 - lim (\frac{3 x + 8}{x + 5})

\infty

解答ステップ

x \to - 5 - lim (\frac{3 x + 8}{x + 5})

\frac{3 x + 8}{x + 5} = (3 x + 8) \frac{1}{x + 5}

= x \to - 5 - lim ((3 x + 8) \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 (3 x + 8) \cdot x \to - 5 - lim (\frac{1}{x + 5})

x \to - 5 - lim (3 x + 8) = - 7

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

= (- 7) (- \infty)

無限大の特性を適用する:

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

= \infty