limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x}

解

x \to \infty lim (3 x^{3} + 3 x^{2} - x)

\infty

解答ステップ

x \to \infty lim (3 x^{3} + 3 x^{2} - x)

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定形式の場合を除く

= 3 x \to \infty lim (x^{3} + 3 x^{2} - x)

無限大の特性を適用する:

x \to \infty lim (a x^{n} + \dots + b x + c) = \infty, a > 0,

n is odd

a = 1, n = 3

= 3 \infty

無限大の特性を適用する:

\infty^{c} = \infty

= \infty