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

The limit as t approaches 0+of (sin(2t))/t is 2

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limit as t approaches 0+of (sin(2t))/t

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

2

Solution steps

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

Apply L'Hopital's Rule

: t \to 0 + lim (\frac{cos ( 2 t ) \cdot 2}{1})

= t \to 0 + lim (\frac{cos ( 2 t ) \cdot 2}{1})

Plug in the value

t = 0

= \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

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