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

解

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

\frac{3}{10}

十進法表記

0.3

解答ステップ

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

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{sec ^{2} ( 10 x ) \cdot 10})

値を挿入する

x = 0

= \frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 10 \cdot 0 ) \cdot 10}

簡素化

\frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 10 \cdot 0 ) \cdot 10} : \frac{3}{10}

= \frac{3}{10}