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

解

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

\infty

解答ステップ

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

最高の分母べき乗で割る:

1 - \frac{1}{x}

= x \to 0 - lim (1 - \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

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

x \to 0 - lim (1) = 1

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

= 1 - (- \infty)

簡素化

1 - (- \infty) : \infty

= \infty