limit as x approaches-3+of-(x^2)/(3x+9)

解

x \to - 3 + lim (- \frac{x ^{2}}{3 x + 9})

- \infty

解答ステップ

x \to - 3 + lim (- \frac{x ^{2}}{3 x + 9})

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

= - x \to - 3 + lim (\frac{x ^{2}}{3 x + 9})

\frac{x ^{2}}{3 x + 9} = x^{2} \frac{1}{3 x + 9}

= - x \to - 3 + lim (x^{2} \frac{1}{3 x + 9})

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 - 3 + lim (x^{2}) \cdot x \to - 3 + lim (\frac{1}{3 x + 9})

x \to - 3 + lim (x^{2}) = 9

x \to - 3 + lim (\frac{1}{3 x + 9}) = \infty

= - 9 \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty