What is the limit as t approaches 0 of (sin(4t))/t ?

The limit as t approaches 0 of (sin(4t))/t is 4

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limit as t approaches 0 of (sin(4t))/t

t \to 0 lim (\frac{sin ( 4 t )}{t})

4

Solution steps

t \to 0 lim (\frac{sin ( 4 t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{cos ( 4 t ) \cdot 4}{1})

= t \to 0 lim (\frac{cos ( 4 t ) \cdot 4}{1})

Plug in the value

t = 0

= \frac{cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 4

= 4

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What is the limit as t approaches 0 of (sin(4t))/t ?
The limit as t approaches 0 of (sin(4t))/t is 4