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

解

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

- \infty

解答ステップ

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

\frac{x}{4 - x ^{2}} = x \frac{1}{4 - x ^{2}}

= x \to 2 + lim (x \frac{1}{4 - 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

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

x \to 2 + lim (x) = 2

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

= 2 (- \infty)

無限大の特性を適用する:

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

= - \infty