Limit of sin(3x)/sin(5x) as x→0

[PirateFan308]

Homework Statement

Find $$\lim_{x\rightarrow 0} {\frac{\sin(3x)}{\sin(5x)}}$$

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.

 

[Mark44]

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

 

[LCKurtz]

This thread is strikingly similar to this one:

https://www.physicsforums.com/showthread.php?t=554581

with both posters having 44 or 45 posts. Interesting coincidence.

 

[PirateFan308]

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