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

解

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

- \infty

解答ステップ

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

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

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

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}{x + 1})

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

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

= 1 \cdot (- \infty)

無限大の特性を適用する:

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

= - \infty