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

解

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

- \infty

解答ステップ

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

\frac{x ^{3} + 9}{x + 3} = (x^{3} + 9) \frac{1}{x + 3}

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

x \to - 3 + lim (x^{3} + 9) = - 18

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

= (- 18) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty