limit as x approaches infinity of ((e^x+e^{-x}))/2

解

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

\infty

解答ステップ

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

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

= \frac{1}{2} \cdot 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

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

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

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

= \frac{1}{2} (\infty + 0)

簡素化

\frac{1}{2} (\infty + 0) : \infty

= \infty