Question

Limit help!

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

Answer 1

\[\frac{ 3 }{ 2 }\]

Answer 2

Did you make it 3/2 * [(sin x)/x] ?

Answer 3

You can use L'hopitals Rule, take derivative of top and bottom then plug in 0

Answer 4

Oh okay! Thanks! c:

Answer 5

Alternatively, you use the fact that \(\displaystyle\lim_{t\to0}\dfrac{\sin at}{at}=1\), after some algebraic manipulation:
\[\lim_{t\to0}\frac{\sin 3t}{2t}=\frac{1}{2}\cdot\frac{3}{3}\lim_{t\to0}\frac{\sin 3t}{t}=\frac{3}{2}\lim_{t\to0}\frac{\sin 3t}{3t}\]