limit as x approaches 3-of (x-4)/(x-3)

解

x \to 3 - lim (\frac{x - 4}{x - 3})

\infty

解答ステップ

x \to 3 - lim (\frac{x - 4}{x - 3})

\frac{x - 4}{x - 3} = (x - 4) \frac{1}{x - 3}

= x \to 3 - lim ((x - 4) \frac{1}{x - 3})

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 3 - lim (x - 4) \cdot x \to 3 - lim (\frac{1}{x - 3})

x \to 3 - lim (x - 4) = - 1

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

= (- 1) (- \infty)

無限大の特性を適用する:

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

= \infty