limit as x approaches 5+of (x+2)/(5-x)

解

x \to 5 + lim (\frac{x + 2}{5 - x})

- \infty

解答ステップ

x \to 5 + lim (\frac{x + 2}{5 - x})

\frac{x + 2}{5 - x} = (x + 2) \frac{1}{5 - x}

= x \to 5 + lim ((x + 2) \frac{1}{5 - 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 5 + lim (x + 2) \cdot x \to 5 + lim (\frac{1}{5 - x})

x \to 5 + lim (x + 2) = 7

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

= 7 (- \infty)

無限大の特性を適用する:

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

= - \infty