limit as x approaches-infinity of e^x+e^{-x}

解

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

\infty

解答ステップ

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

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

不定形式の場合を除く

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

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

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

= 0 + \infty

無限大の特性を適用する:

c + \infty = \infty

= \infty