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

解

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

- \infty

解答ステップ

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

最高の分母べき乗で割る:

\frac{1}{x} - \frac{1}{x ^{2}}

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

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

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

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

= - \infty - \infty

無限大の特性を適用する:

- \infty - \infty = - \infty

= - \infty