limit as x approaches 0+of (x^2+3x+4)/x

解

x \to 0 + lim (\frac{x ^{2} + 3 x + 4}{x})

\infty

解答ステップ

x \to 0 + lim (\frac{x ^{2} + 3 x + 4}{x})

最高の分母べき乗で割る:

x + 3 + \frac{4}{x}

= x \to 0 + lim (x + 3 + \frac{4}{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 0 + lim (x) + x \to 0 + lim (3) + x \to 0 + lim (\frac{4}{x})

x \to 0 + lim (x) = 0

x \to 0 + lim (3) = 3

x \to 0 + lim (\frac{4}{x}) = \infty

= 0 + 3 + \infty

無限大の特性を適用する:

c + \infty = \infty

= \infty