limit as x approaches infinity of-xe^{-x^2}2-e^{-x^2}

解

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

0

解答ステップ

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

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

x \to \infty lim (x e^{- x^{2}} \cdot 2) = 0

x \to \infty lim (e^{- x^{2}}) = 0

= - 0 - 0

簡素化

= 0