limit as x approaches-7-of (x+3)/(x+7)

解

x \to - 7 - lim (\frac{x + 3}{x + 7})

\infty

解答ステップ

x \to - 7 - lim (\frac{x + 3}{x + 7})

\frac{x + 3}{x + 7} = (x + 3) \frac{1}{x + 7}

= x \to - 7 - lim ((x + 3) \frac{1}{x + 7})

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 - 7 - lim (x + 3) \cdot x \to - 7 - lim (\frac{1}{x + 7})

x \to - 7 - lim (x + 3) = - 4

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

= (- 4) (- \infty)

無限大の特性を適用する:

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

= \infty