# Limit of sin2x/sin3x

1. Oct 9, 2011

### Nano-Passion

1. The problem statement, all variables and given/known data

Determine the limit of

$\lim_{x \to 0} \frac {sin2x}{sin3x}$

2. Relevant equations

Hint: Find $\lim_{x\to 0} (\frac{2 sin 2x}{2x}) (\frac{3x}{3 sin 3x})$
3. The attempt at a solution

I've been blankly staring at it not knowing where to start. I think the only thing that the hint manages to do is to confuse me.

Any help on helping me to start it? I don't understand the hint.

2. Oct 9, 2011

### ehild

Do you not what is $$\lim _{x \to 0} \frac{sin(x)}{x}$$?

ehild

3. Oct 9, 2011

### vela

Staff Emeritus
In your book or notes, you should find how to evaluate
$$\lim_{x \to 0} \frac{\sin x}{x}$$

4. Oct 9, 2011

### Nano-Passion

Yes they are equal to one, but they aren't asking for $$\lim_{x \to 0} \frac {sinx}{x}$$

They are asking for $$\lim_ {x \to 0} \frac{sin2x}{sin3x}$$

5. Oct 9, 2011

### vela

Staff Emeritus
And you see absolutely no connection to that limit and the hint?

6. Oct 9, 2011

### Nano-Passion

Ohhhhhh !

Its funny how someone can say so little yet help so much hehe. Thanks, I got it now.

7. Oct 9, 2011

8. Oct 9, 2011

### vela

Staff Emeritus
I think we've all had those moments where we fail to see what in hindsight seems so obvious.

9. Oct 9, 2011

### Nano-Passion

Thank you for your help by the way:)

10. Oct 9, 2011

### HallsofIvy

Staff Emeritus
For a more "formal" look, let u= 2x so that you have
$$\lim_{x\to 0}\frac{sin(2x)}{2x}= \lim_{u\to 0}\frac{sin(u)}{u}$$

11. Oct 9, 2011

### Nano-Passion

Hey halls, thanks for the suggestion. Will keep in mind in the future. ^.^