limit as x approaches-5-of (4x^2-12)/(x+5)

解

x \to - 5 - lim (\frac{4 x ^{2} - 12}{x + 5})

- \infty

解答ステップ

x \to - 5 - lim (\frac{4 x ^{2} - 12}{x + 5})

\frac{4 x ^{2} - 12}{x + 5} = (4 x^{2} - 12) \frac{1}{x + 5}

= x \to - 5 - lim ((4 x^{2} - 12) \frac{1}{x + 5})

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 - 5 - lim (4 x^{2} - 12) \cdot x \to - 5 - lim (\frac{1}{x + 5})

x \to - 5 - lim (4 x^{2} - 12) = 88

x \to - 5 - lim (\frac{1}{x + 5}) = - \infty

= 88 (- \infty)

無限大の特性を適用する:

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

= - \infty