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

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Homework Help Overview

The problem involves finding the limit of the expression xsin(1/(x^2)) as x approaches 0, which falls under the subject area of limits in calculus, particularly focusing on trigonometric functions and their behavior near specific points.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant suggests that the limit approaches 0 based on the oscillatory nature of the sine function, while another introduces the concept of the Squeeze Theorem as a potential method for analysis. There is a question raised about the permissibility of using this theorem in the context of the problem.

Discussion Status

The discussion is currently exploring different approaches to the limit, with some participants providing insights into the Squeeze Theorem and its relevance. There is acknowledgment of the theorem's applicability, but no consensus or resolution has been reached yet.

Contextual Notes

Participants are considering the implications of using the Squeeze Theorem and whether it is allowed within the constraints of the homework guidelines.

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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.
 
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The name of the test you want to do is sometimes called the 'squeeze theorem'.
 
Are you allowed to use the Squeeze (or Sandwich) Theorem?
 
Ah yes. Thanks a lot for that.
 

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