Question

lim 0 goes to theta of sin(3 theta)/(theta)

Answer 1

Welcome to Openstudy!
This is the question right?
\[\lim_{x \rightarrow 0} \frac{\sin \theta}{\theta}\]

Answer 2

Yes!

Answer 3

lim theta goes to 0

Answer 4

\[\lim_{\theta \rightarrow 0} \frac{\sin 3 \theta}{\theta}\]

Answer 5

Yeah that's the question

Answer 6

theta is measured in radians

Answer 7

@SithsAndGiggles This is simple for you

Answer 8

I must estimate the limit

Answer 9

Recall that
\[\lim_{\theta\to0}\frac{\sin a\theta}{a\theta}=1\]
How can you get a 3 in the denominator without fundamentally altering the function?

Answer 10

I'm not sure

Answer 11

Well if you were to multiply by 1, you'd have the same thing right?

Fortunately for use, \(\dfrac{3}{3}=1\), so
\[\frac{\sin3\theta}{\theta}=\frac{\sin3\theta}{\theta}\cdot\frac{3}{3}\]

Answer 12

I have that...not sure where to go from there

Answer 13

Then you also have
\[3\lim_{\theta\to0}\frac{\sin3\theta}{3\theta}\]

Answer 14

What's the next step?

Answer 15

See the previous comment:

\(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles
Recall that
\[\lim_{\theta\to0}\frac{\sin a\theta}{a\theta}=1\]
\(\color{blue}{\text{End of Quote}}\)

Answer 16

Got it, the answer is 3