limit as x approaches-8-of (-5x+2)/(x+8)

解

x \to - 8 - lim (\frac{- 5 x + 2}{x + 8})

- \infty

解答ステップ

x \to - 8 - lim (\frac{- 5 x + 2}{x + 8})

\frac{- 5 x + 2}{x + 8} = (- 5 x + 2) \frac{1}{x + 8}

= x \to - 8 - lim ((- 5 x + 2) \frac{1}{x + 8})

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 - 8 - lim (- 5 x + 2) \cdot x \to - 8 - lim (\frac{1}{x + 8})

x \to - 8 - lim (- 5 x + 2) = 42

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

= 42 (- \infty)

無限大の特性を適用する:

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

= - \infty