limit as x approaches 0 of (cos(3x)tan(3x))/x

解

x \to 0 lim (\frac{cos ( 3 x ) tan ( 3 x )}{x})

3

解答ステップ

x \to 0 lim (\frac{cos ( 3 x ) tan ( 3 x )}{x})

cos (3 x) tan (3 x) = sin (3 x)

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

ロピタルの定理を適用する

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

値を挿入する

x = 0

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

簡素化

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

= 3