limit as t approaches 0 of (tan^2(3t))/(2t)

解

t \to 0 lim (\frac{tan ^{2} ( 3 t )}{2 t})

0

解答ステップ

t \to 0 lim (\frac{tan ^{2} ( 3 t )}{2 t})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot t \to 0 lim (\frac{tan ^{2} ( 3 t )}{t})

ロピタルの定理を適用する

= \frac{1}{2} \cdot t \to 0 lim (\frac{6 sec ^{2} ( 3 t ) tan ( 3 t )}{1})

値を挿入する

t = 0

= \frac{1}{2} \cdot \frac{6 sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )}{1}

簡素化

\frac{1}{2} \cdot \frac{6 sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )}{1} : 0

= 0