What is the limit as t approaches 0 of (tan(10t))/(sin(2t)) ?

The limit as t approaches 0 of (tan(10t))/(sin(2t)) is 5

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limit as t approaches 0 of (tan(10t))/(sin(2t))

t \to 0 lim (\frac{tan ( 10 t )}{sin ( 2 t )})

5

Solution steps

t \to 0 lim (\frac{tan ( 10 t )}{sin ( 2 t )})

Apply L'Hopital's Rule

= t \to 0 lim (\frac{sec ^{2} ( 10 t ) \cdot 10}{cos ( 2 t ) \cdot 2})

Plug in the value

t = 0

= \frac{sec ^{2} ( 10 \cdot 0 ) \cdot 10}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{sec ^{2} ( 10 \cdot 0 ) \cdot 10}{cos ( 2 \cdot 0 ) \cdot 2} : 5

= 5

What is the limit as t approaches 0 of (tan(10t))/(sin(2t)) ?
The limit as t approaches 0 of (tan(10t))/(sin(2t)) is 5