limit as x approaches 0-of (3x-1)/(2x)

解

x \to 0 - lim (\frac{3 x - 1}{2 x})

\infty

解答ステップ

x \to 0 - lim (\frac{3 x - 1}{2 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot x \to 0 - lim (\frac{3 x - 1}{x})

最高の分母べき乗で割る:

3 - \frac{1}{x}

= \frac{1}{2} \cdot x \to 0 - lim (3 - \frac{1}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定形式の場合を除く

= \frac{1}{2} (x \to 0 - lim (3) - x \to 0 - lim (\frac{1}{x}))

x \to 0 - lim (3) = 3

x \to 0 - lim (\frac{1}{x}) = - \infty

= \frac{1}{2} (3 - (- \infty))

無限大の特性を適用する:

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

= \infty