limit as x approaches-2-of (3x-1)/(x+2)

解

x \to - 2 - lim (\frac{3 x - 1}{x + 2})

\infty

解答ステップ

x \to - 2 - lim (\frac{3 x - 1}{x + 2})

\frac{3 x - 1}{x + 2} = (3 x - 1) \frac{1}{x + 2}

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

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 - 2 - lim (3 x - 1) \cdot x \to - 2 - lim (\frac{1}{x + 2})

x \to - 2 - lim (3 x - 1) = - 7

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

= (- 7) (- \infty)

無限大の特性を適用する:

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

= \infty