limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2))

解

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

- 1

解答ステップ

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

拡張

\frac{5 + 2 x}{9 + 4 x ^{2}} : \frac{5}{9 + 4 x ^{2}} + \frac{2 x}{9 + 4 x ^{2}}

= x \to - \infty lim (\frac{5}{9 + 4 x ^{2}} + \frac{2 x}{9 + 4 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 (\frac{5}{9 + 4 x ^{2}}) + x \to - \infty lim (\frac{2 x}{9 + 4 x ^{2}})

x \to - \infty lim (\frac{5}{9 + 4 x ^{2}}) = 0

x \to - \infty lim (\frac{2 x}{9 + 4 x ^{2}}) = - 1

= 0 - 1

簡素化

= - 1