What is the limit of sin|x|/x as x approaches 0?

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Homework Help Overview

The discussion revolves around finding the limit of the expression sin|x|/x as x approaches 0, which falls under the subject area of calculus, specifically limits and continuity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand why the limit might not exist and contrasts it with the known limit of sin(x)/x. Some participants suggest examining one-sided limits to clarify the situation.

Discussion Status

Participants are exploring the concept of one-sided limits, with some guidance provided on how to approach the problem by considering the behavior of the function as x approaches 0 from both the positive and negative directions. There is an ongoing inquiry into the nature of these limits.

Contextual Notes

The original poster expresses uncertainty about the one-sided limits and their implications for the overall limit, indicating a need for further clarification on this aspect.

math2010
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Homework Statement



I want to find the limit:

\lim_{x\to 0}\frac{sin|x|}{x}


The Attempt at a Solution



I know that the answer must be "limit doesn't exist" but I don't know how to arrive at that answer. I know that \lim_{x\to 0}\frac{sinx}{x}=1 but apparently it's a very different situation. Can anyone show me how to find this limit?
 
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Look at the two one-sided limits, and see if they are the same or different.
 
Mark44 said:
Look at the two one-sided limits, and see if they are the same or different.

What are the two one sided limits? That's what I don't get!
 
lim x -->0+
lim x -->0-

For the first, |x| = x
For the second, |x| = -x
 

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