limit as x approaches 10+of (x^3)/(x-10)

解

x \to 10 + lim (\frac{x ^{3}}{x - 10})

\infty

解答ステップ

x \to 10 + lim (\frac{x ^{3}}{x - 10})

\frac{x ^{3}}{x - 10} = x^{3} \frac{1}{x - 10}

= x \to 10 + lim (x^{3} \frac{1}{x - 10})

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 10 + lim (x^{3}) \cdot x \to 10 + lim (\frac{1}{x - 10})

x \to 10 + lim (x^{3}) = 1000

x \to 10 + lim (\frac{1}{x - 10}) = \infty

= 1000 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty