# Limits when there is a sine function?

## Homework Statement

lim x-> ∞ xsin(1/x)

## 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

## Answers and Replies

vanhees71
Science Advisor
Gold Member
Hint
$$x \sin(1/x)=\frac{\sin(1/x)}{1/x}.$$

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

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

Mark44
Mentor
I wouldn't. This limit is related to this well-known limit
$$\lim_{t \to 0}\frac{sin(t)}{t}$$

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

What do you mean?

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