limit as x approaches infinity of e^x-ex

解

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

\infty

解答ステップ

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

e^{x}

を

e^{x} - e x : e^{x} (1 - \frac{e x}{e ^{x}})

からくくり出す

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

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

不定形式の場合を除く

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

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

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

= \infty \cdot 1

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty