limit as x approaches 1-of (2x+1)/(x-1)

解

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

- \infty

解答ステップ

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

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

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

x \to 1 - lim (2 x + 1) = 3

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

= 3 (- \infty)

無限大の特性を適用する:

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

= - \infty