Trigonometric Limits: Find xsin(1/(x^2)) Limit as x->0

[*FaerieLight*]

Homework Statement

Find the limit as x approaches 0 of xsin(1/(x^2))

Homework Equations

The Attempt at a Solution

I think this goes to 0, because the sine component just oscillates between 1 and -1, and gets multiplied by 0, for all x. I don't know how to show this using limit laws/algebraically.

 

[Dick]

The name of the test you want to do is sometimes called the 'squeeze theorem'.

 

[JThompson]

Are you allowed to use the Squeeze (or Sandwich) Theorem?

 

[*FaerieLight*]

Ah yes. Thanks a lot for that.