Limits when there is a sine function?

[applestrudle]

Homework Statement

lim x-> ∞ xsin(1/x)

Homework Equations

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

 

[vanhees71]

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

 

[applestrudle]

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

Ahh thank you! Then you use l'hospital's Rule?

 

[Mark44]

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

 

[applestrudle]

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

What do you mean?

 

[Legaldose]

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