limit as x approaches 0 of (sin(5x))/(tan(6x))

解

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

\frac{5}{6}

十進法表記

0.83333 \dots

解答ステップ

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{sec ^{2} ( 6 x ) \cdot 6})

値を挿入する

x = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 6 \cdot 0 ) \cdot 6}

簡素化

\frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 6 \cdot 0 ) \cdot 6} : \frac{5}{6}

= \frac{5}{6}