limit as x approaches 4-of (x-5)/(x-4)

解

x \to 4 - lim (\frac{x - 5}{x - 4})

\infty

解答ステップ

x \to 4 - lim (\frac{x - 5}{x - 4})

\frac{x - 5}{x - 4} = (x - 5) \frac{1}{x - 4}

= x \to 4 - lim ((x - 5) \frac{1}{x - 4})

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 4 - lim (x - 5) \cdot x \to 4 - lim (\frac{1}{x - 4})

x \to 4 - lim (x - 5) = - 1

x \to 4 - lim (\frac{1}{x - 4}) = - \infty

= (- 1) (- \infty)

無限大の特性を適用する:

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

= \infty