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

解

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

\infty

解答ステップ

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

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

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

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

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

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

= 5 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty