limit as x approaches 0 of (sin(x))/(5x)

解

x \to 0 lim (\frac{sin ( x )}{5 x})

\frac{1}{5}

十進法表記

0.2

解答ステップ

x \to 0 lim (\frac{sin ( x )}{5 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{5} \cdot x \to 0 lim (\frac{sin ( x )}{x})

ロピタルの定理を適用する

= \frac{1}{5} \cdot x \to 0 lim (\frac{cos ( x )}{1})

値を挿入する

x = 0

= \frac{1}{5} \cdot \frac{cos ( 0 )}{1}

簡素化

\frac{1}{5} \cdot \frac{cos ( 0 )}{1} : \frac{1}{5}

= \frac{1}{5}