limit as x approaches 8-of x/(x^2-64)

解

x \to 8 - lim (\frac{x}{x ^{2} - 64})

- \infty

解答ステップ

x \to 8 - lim (\frac{x}{x ^{2} - 64})

\frac{x}{x ^{2} - 64} = x \frac{1}{x ^{2} - 64}

= x \to 8 - lim (x \frac{1}{x ^{2} - 64})

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 8 - lim (x) \cdot x \to 8 - lim (\frac{1}{x ^{2} - 64})

x \to 8 - lim (x) = 8

x \to 8 - lim (\frac{1}{x ^{2} - 64}) = - \infty

= 8 (- \infty)

無限大の特性を適用する:

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

= - \infty