limit as b approaches infinity of e^{-b}

解

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

0

解答ステップ

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

簡素化

e^{- b} : \frac{1}{e ^{b}}

= b \to \infty lim (\frac{1}{e ^{b}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{b \to \infty} ( 1 )}{lim _{b \to \infty} ( e ^{b} )}

b \to \infty lim (1) = 1

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

= \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0