limit as x approaches 0 of (3x)/(sin(10x))

解

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

\frac{3}{10}

十進法表記

0.3

解答ステップ

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

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

= 3 \cdot x \to 0 lim (\frac{x}{sin ( 10 x )})

ロピタルの定理を適用する

= 3 \cdot x \to 0 lim (\frac{1}{cos ( 10 x ) \cdot 10})

値を挿入する

x = 0

= 3 \cdot \frac{1}{cos ( 10 \cdot 0 ) \cdot 10}

簡素化

3 \cdot \frac{1}{cos ( 10 \cdot 0 ) \cdot 10} : \frac{3}{10}

= \frac{3}{10}