limit as x approaches 4+of (x-1)/(4-x)

解

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

- \infty

解答ステップ

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

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

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

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

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

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

= 3 (- \infty)

無限大の特性を適用する:

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

= - \infty