# Find the limit.

1. Feb 6, 2008

### Oneiromancy

lim y->0 (sin 3y * cot 5y)/(y * cot 4y)

Tricky problem to me. I understand what to do if the problem was something like sin 5x / 4x.

Last edited: Feb 6, 2008
2. Feb 6, 2008

### sutupidmath

Well first rewrite cot in terms of sin and cosine, and look to come up with something sinx/x when x-->0 to some parts of it at least.

3. Feb 6, 2008

### rocomath

$$\lim_{y\rightarrow 0}\frac{\sin{3y}\cot{5y}}{y\cot{4y}}$$

4. Feb 6, 2008

### Oneiromancy

Correct. Sorry I'm not good at latex.

5. Feb 6, 2008

### rocomath

$$\lim_{y\rightarrow 0}\frac{\sin{3y}}{y}\cdot\frac{\sin{4y}}{\cos{4y}}\cdot\frac{\cos{5y}}{\sin{5y}}$$

How can you manipulate your limit? The left term is very easy.

Last edited: Feb 7, 2008
6. Feb 6, 2008

### Oneiromancy

I know what to do now.

7. Feb 7, 2008

### HallsofIvy

Staff Emeritus
It would be easier if it were sin(3y)/y rather than sin(3x)/y !!!

8. Feb 7, 2008

### rocomath

It was a typo!!!