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

解

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

- \infty

解答ステップ

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

最高の分母べき乗で割る:

x^{2} + \frac{3}{x}

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

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

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

= 0 - \infty

無限大の特性を適用する:

c - \infty = - \infty

= - \infty