limit as x approaches 0 of (x+sin(x))/x

解

x \to 0 lim (\frac{x + sin ( x )}{x})

2

解答ステップ

x \to 0 lim (\frac{x + sin ( x )}{x})

最高の分母べき乗で割る:

1 + \frac{sin ( x )}{x}

= x \to 0 lim (1 + \frac{sin ( x )}{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 (1) + x \to 0 lim (\frac{sin ( x )}{x})

x \to 0 lim (1) = 1

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

= 1 + 1

簡素化

= 2