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人気のある微分積分 >

limit as x approaches-infinity of-x^2e^x

解

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

解

0

解答ステップ

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

ロピタル向けに書き換える

= - x \to - \infty lim (\frac{x ^{2}}{\frac{1}{e ^{x}}})

ロピタルの定理を適用する

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

ロピタルの定理を適用する

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

簡素化

\frac{2}{e ^{- x}} : 2 e^{x}

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

共通限度を適用する:

x \to - \infty lim (e^{x}) = 0

= - 2 \cdot 0

簡素化

= 0

グラフ

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