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

解答

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

\infty

求解步骤

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

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

不定型除外

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

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

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

= 0 - (- \infty)

化简

0 - (- \infty) : \infty

= \infty

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