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受欢迎的微积分 >

limit as x approaches-infinity of x^4e^x

解答

x \to - \infty lim (x^{4} e^{x})

解答

0

求解步骤

x \to - \infty lim (x^{4} e^{x})

改写以应用洛必达法则

= x \to - \infty lim (\frac{x ^{4}}{\frac{1}{e ^{x}}})

使用洛必达法则

= x \to - \infty lim (\frac{4 x ^{3}}{- e ^{- x}})

使用洛必达法则

= x \to - \infty lim (\frac{12 x ^{2}}{e ^{- x}})

使用洛必达法则

= x \to - \infty lim (\frac{24 x}{- e ^{- x}})

使用洛必达法则

= x \to - \infty lim (\frac{24}{e ^{- x}})

化简

\frac{24}{e ^{- x}} : 24 e^{x}

= x \to - \infty lim (24 e^{x})

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

= 24 \cdot x \to - \infty lim (e^{x})

运用一般极限法则:

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

= 24 \cdot 0

化简

= 0

作图

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