limit as t approaches 0 of (tan(6t))/(sin(2t))

解

t \to 0 lim (\frac{tan ( 6 t )}{sin ( 2 t )})

3

解答ステップ

t \to 0 lim (\frac{tan ( 6 t )}{sin ( 2 t )})

ロピタルの定理を適用する

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

値を挿入する

t = 0

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

簡素化

\frac{sec ^{2} ( 6 \cdot 0 ) \cdot 6}{cos ( 2 \cdot 0 ) \cdot 2} : 3

= 3