# Limit of sin(3x)/sin(5x) as x→0

1. Nov 28, 2011

### PirateFan308

1. The problem statement, all variables and given/known data
Find $$\lim_{x\rightarrow 0} {\frac{\sin(3x)}{\sin(5x)}}$$

3. The attempt at a solution
I know that the limit equals 0.6 (by typing it into my calculator), but I have no idea how to prove this, or even where to start. I know that sin is continuous, so I theoretically should be able to just plug it in, but obviously this doesn't work because it isn't divisible by 0.

2. Nov 28, 2011

### Staff: Mentor

Try multiplying by 3x/(3x) and 5x/(5x), and placing the numerators and denominators strategically. The basic idea is that $\lim_{u \to 0} \frac{sin u}{u} = 1$

3. Nov 28, 2011

### LCKurtz

4. Nov 28, 2011

### PirateFan308

Thank you! I can't believe I didn't think of that answer - that helped me figure out the later questions as well.