limit as x approaches-infinity of x^2e^{-3x}

解

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

\infty

解答ステップ

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

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

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

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

= \infty \cdot \infty

無限大の特性を適用する:

\infty \infty = \infty

= \infty