limit as x approaches infinity of ((e^{2x}-8-19x))/((19x)^2)

解

x \to \infty lim (\frac{( e ^{2 x} - 8 - 19 x )}{( 19 x ) ^{2}})

\infty

解答ステップ

x \to \infty lim (\frac{e ^{2 x} - 8 - 19 x}{( 19 x ) ^{2}})

拡張

\frac{e ^{2 x} - 8 - 19 x}{( 19 x ) ^{2}} : \frac{e ^{2 x}}{361 x ^{2}} - \frac{8}{361 x ^{2}} - \frac{1}{19 x}

= x \to \infty lim (\frac{e ^{2 x}}{361 x ^{2}} - \frac{8}{361 x ^{2}} - \frac{1}{19 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

= x \to \infty lim (\frac{e ^{2 x}}{361 x ^{2}}) - x \to \infty lim (\frac{8}{361 x ^{2}}) - x \to \infty lim (\frac{1}{19 x})

x \to \infty lim (\frac{e ^{2 x}}{361 x ^{2}}) = \infty

x \to \infty lim (\frac{8}{361 x ^{2}}) = 0

x \to \infty lim (\frac{1}{19 x}) = 0

= \infty - 0 - 0

簡素化

\infty - 0 - 0 : \infty

= \infty