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

解答

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

\infty

求解步骤

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}

不定型除外

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

运用无穷大属性:

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

n is odd

a = 1, n = 3

= 3 \infty

运用无穷大属性:

\infty^{c} = \infty

= \infty

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