limit as x approaches infinity of (sqrt(x+a)+sqrt(x+b))/(sqrt(x))

解

x \to \infty lim (\frac{x + a + x + b}{x})

2

解答ステップ

x \to \infty lim (\frac{x + a + x + b}{x})

拡張

\frac{x + a + x + b}{x} : \frac{x + a}{x} + \frac{x + b}{x}

= x \to \infty lim (\frac{x + a}{x} + \frac{x + b}{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{x + a}{x}) + x \to \infty lim (\frac{x + b}{x})

x \to \infty lim (\frac{x + a}{x}) = 1

x \to \infty lim (\frac{x + b}{x}) = 1

= 1 + 1

簡素化

= 2