limit as x approaches infinity of x/(e^{-x)}

解答

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

\infty

求解步骤

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

化简

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

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

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

不定型除外

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

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

x \to \infty lim (x) = \infty

= \infty \cdot \infty

运用无穷大属性:

\infty \infty = \infty

= \infty

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