limit as x approaches-1-of (x^2)/(1+x^3)

解

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

- \infty

解答ステップ

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

\frac{x ^{2}}{1 + x ^{3}} = x^{2} \frac{1}{1 + x ^{3}}

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

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

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

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

= 1 \cdot (- \infty)

無限大の特性を適用する:

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

= - \infty