# Limits when there is a sine function?

1. Oct 11, 2013

### applestrudle

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

lim x-> ∞ xsin(1/x)

2. Relevant equations

3. The attempt at a solution

I know that this is an ∞.0 type limit but I can't figure out how to change the sin function.

Thank you

2. Oct 11, 2013

### vanhees71

Hint
$$x \sin(1/x)=\frac{\sin(1/x)}{1/x}.$$

3. Oct 11, 2013

### applestrudle

Ahh thank you! Then you use L'Hopitals Rule?

4. Oct 11, 2013

### Staff: Mentor

I wouldn't. This limit is related to this well-known limit
$$\lim_{t \to 0}\frac{sin(t)}{t}$$

5. Oct 11, 2013

### applestrudle

What do you mean?

6. Oct 11, 2013

### Legaldose

Hint 2: Use a substitution, then figure out what the appropriate change in the limit would be.