limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4}

解

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

- \frac{3}{5}

十進法表記

- 0.6

解答ステップ

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

e^{- x}

で割る

: \frac{2 e ^{x} - 3}{5 - 4 e ^{x}}

= x \to - \infty lim (\frac{2 e ^{x} - 3}{5 - 4 e ^{x}})

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 _{x \to - \infty} ( 2 e ^{x} - 3 )}{lim _{x \to - \infty} ( 5 - 4 e ^{x} )}

x \to - \infty lim (2 e^{x} - 3) = - 3

x \to - \infty lim (5 - 4 e^{x}) = 5

= \frac{- 3}{5}

簡素化

= - \frac{3}{5}