limit as x approaches 0 of (sin(7x))/(tan(11x))

解

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

\frac{7}{11}

十進法表記

0.63636 \dots

解答ステップ

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 11 x ) \cdot 11})

値を挿入する

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11}

簡素化

\frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11} : \frac{7}{11}

= \frac{7}{11}