What is the limit as t approaches 0 of (tan^2(3t))/(2t) ?

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

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

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

0

Solution steps

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})

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= 0

\int e^{\frac{x}{7}} d x

\int cos (2 n t) d t

ln (s^{2} + 9)

\int_{1}^{7} t ln (t) d t

\frac{3}{s ( s ^{2} + s + 5 )}

What is the limit as t approaches 0 of (tan^2(3t))/(2t) ?
The limit as t approaches 0 of (tan^2(3t))/(2t) is 0