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

解

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

\infty

解答ステップ

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

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

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

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

= 2 \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

= 2 \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

= 2 \cdot 3 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty