limit as x approaches 0 of (6sin(3x))/x

解

x \to 0 lim (\frac{6 sin ( 3 x )}{x})

18

解答ステップ

x \to 0 lim (\frac{6 sin ( 3 x )}{x})

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

= 6 \cdot x \to 0 lim (\frac{sin ( 3 x )}{x})

ロピタルの定理を適用する

= 6 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

値を挿入する

x = 0

= 6 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

簡素化

6 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 18

= 18