limit as x approaches 6-of (x^6)/(x-6)

解

x \to 6 - lim (\frac{x ^{6}}{x - 6})

- \infty

解答ステップ

x \to 6 - lim (\frac{x ^{6}}{x - 6})

\frac{x ^{6}}{x - 6} = x^{6} \frac{1}{x - 6}

= x \to 6 - lim (x^{6} \frac{1}{x - 6})

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 6 - lim (x^{6}) \cdot x \to 6 - lim (\frac{1}{x - 6})

x \to 6 - lim (x^{6}) = 46656

x \to 6 - lim (\frac{1}{x - 6}) = - \infty

= 46656 (- \infty)

無限大の特性を適用する:

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

= - \infty