limit as x approaches-8+of ((x+7))/(x+8)

解

x \to - 8 + lim (\frac{( x + 7 )}{x + 8})

- \infty

解答ステップ

x \to - 8 + lim (\frac{x + 7}{x + 8})

\frac{x + 7}{x + 8} = (x + 7) \frac{1}{x + 8}

= x \to - 8 + lim ((x + 7) \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 (x + 7) \cdot x \to - 8 + lim (\frac{1}{x + 8})

x \to - 8 + lim (x + 7) = - 1

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

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty