limit as t approaches 0 of (sin(3t)+4t)/(tsec(t))

解

t \to 0 lim (\frac{sin ( 3 t ) + 4 t}{t sec ( t )})

7

解答ステップ

t \to 0 lim (\frac{sin ( 3 t ) + 4 t}{t sec ( t )})

ロピタルの定理を適用する

= t \to 0 lim (\frac{cos ( 3 t ) \cdot 3 + 4}{sec ( t ) + t sec ( t ) tan ( t )})

値を挿入する

t = 0

= \frac{cos ( 3 \cdot 0 ) \cdot 3 + 4}{sec ( 0 ) + 0 \cdot sec ( 0 ) tan ( 0 )}

簡素化

\frac{cos ( 3 \cdot 0 ) \cdot 3 + 4}{sec ( 0 ) + 0 \cdot sec ( 0 ) tan ( 0 )} : 7

= 7