Limit doesn't make sense according to the graph?

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The discussion revolves around the confusion regarding the limits of the absolute value function as x approaches zero from both the positive and negative sides. It is clarified that the limits are incorrectly stated; the correct limit as x approaches zero from either side is actually 0, not 1 or -1. Participants question the validity of the limits presented and suggest that the confusion may stem from mixing up limits with derivatives of the function. The importance of accurately interpreting the graph of |x| is emphasized, as it visually supports the correct limits. Overall, the conversation highlights the need for clarity in understanding limits in calculus.
tahayassen
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From first principles,

\underset { x\rightarrow { 0 }^{ + } }{ lim } |x|=1\\ \underset { x\rightarrow { 0 }^{ - } }{ lim } |x|=-1

But if you look at the graph of |x|, it appears that both limits are approaching 0.

O_O
 
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Incorrect. Why do you think so?
 
arildno said:
Incorrect. Why do you think so?

Are the limits incorrect? My textbook has the proof.

I'll post it as soon as possible.
 
Are you sure you are notr talking about the DERIVATIVE of the absolute value function??
 
arildno said:
Are you sure you are notr talking about the DERIVATIVE of the absolute value function??

Makes so much sense! Thanks.
 

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