limit as x approaches-3-of (4x)/(9-x^2)

解

x \to - 3 - lim (\frac{4 x}{9 - x ^{2}})

\infty

解答ステップ

x \to - 3 - lim (\frac{4 x}{9 - x ^{2}})

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

= 4 \cdot x \to - 3 - lim (\frac{x}{9 - x ^{2}})

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

= 4 \cdot x \to - 3 - lim (x \frac{1}{9 - x ^{2}})

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

= 4 \cdot x \to - 3 - lim (x) \cdot x \to - 3 - lim (\frac{1}{9 - x ^{2}})

x \to - 3 - lim (x) = - 3

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

= 4 (- 3) (- \infty)

無限大の特性を適用する:

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

= \infty