limit as x approaches 1+of (x+5)/(1-x^2)

解

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

- \infty

解答ステップ

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

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

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

x \to 1 + lim (x + 5) = 6

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

= 6 (- \infty)

無限大の特性を適用する:

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

= - \infty