limit as x approaches-infinity of x+3x^{2/3}

解

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

- \infty

解答ステップ

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

x

を

x + 3 x^{\frac{2}{3}} : x (1 + \frac{3 x ^{\frac{2}{3}}}{x})

からくくり出す

= x \to - \infty lim (x (1 + \frac{3 x ^{\frac{2}{3}}}{x}))

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

不定形式の場合を除く

= x \to - \infty lim (x) \cdot x \to - \infty lim (1 + \frac{3 x ^{\frac{2}{3}}}{x})

x \to - \infty lim (x) = - \infty

x \to - \infty lim (1 + \frac{3 x ^{\frac{2}{3}}}{x}) = 1

= (- \infty) \cdot 1

無限大の特性を適用する:

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

= - \infty