What is the limit as t approaches 0 of (1-cos(3t))/t ?

The limit as t approaches 0 of (1-cos(3t))/t is 0

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limit as t approaches 0 of (1-cos(3t))/t

t \to 0 lim (\frac{1 - cos ( 3 t )}{t})

0

Solution steps

t \to 0 lim (\frac{1 - cos ( 3 t )}{t})

Apply L'Hopital's Rule

= t \to 0 lim (\frac{3 sin ( 3 t )}{1})

Plug in the value

t = 0

= \frac{3 sin ( 3 \cdot 0 )}{1}

Simplify

\frac{3 sin ( 3 \cdot 0 )}{1} : 0

= 0

What is the limit as t approaches 0 of (1-cos(3t))/t ?
The limit as t approaches 0 of (1-cos(3t))/t is 0