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

解

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

\infty

解答ステップ

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

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

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

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