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

解

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

\infty

解答ステップ

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

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

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

x \to - 3 + lim (x^{3}) = - 27

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

= (- 27) (- \infty)

無限大の特性を適用する:

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

= \infty