limit as x approaches infinity of ((sin(x)-cos(x)))/x

解

x \to \infty lim (\frac{( sin ( x ) - cos ( x ) )}{x})

0

解答ステップ

x \to \infty lim (\frac{sin ( x ) - cos ( x )}{x})

拡張

\frac{sin ( x ) - cos ( x )}{x} : \frac{sin ( x )}{x} - \frac{cos ( x )}{x}

= x \to \infty lim (\frac{sin ( x )}{x} - \frac{cos ( 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 \infty lim (\frac{sin ( x )}{x}) - x \to \infty lim (\frac{cos ( x )}{x})

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

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

= 0 - 0

簡素化

= 0