What is the limit as t approaches 0 of (tan(6t))/(sin(2t)) ?

The limit as t approaches 0 of (tan(6t))/(sin(2t)) is 3

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

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

3

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= 3

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\int \frac{d t}{t ^{3} t ^{2} - 9} d x

\frac{\partial}{\partial x} ((2 x + 5 y) e^{y})

What is the limit as t approaches 0 of (tan(6t))/(sin(2t)) ?
The limit as t approaches 0 of (tan(6t))/(sin(2t)) is 3