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

解

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

\infty

解答ステップ

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

拡張

\frac{x ^{3} - 2}{x} : x^{2} - \frac{2}{x}

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

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

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

= 0 - (- \infty)

簡素化

0 - (- \infty) : \infty

= \infty