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the question is : is y=|x-1|/(x-1)continuous on (-infi, +infi):

I am wondering why this equation is not continuous when x = 1

I think when x=1, y will be 1

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    $\begingroup$ Did you graph the function? That could be one start in the learning process $\endgroup$ – imranfat Sep 29 '15 at 18:47
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$\lim_{x\to 1^+}\frac{|x-1|}{x-1}=\lim_{x\to 1^+}\frac{x-1}{x-1}=1\color{red}{\neq}\lim_{x\to 1^-}\frac{|x-1|}{x-1}=\lim_{x\to 1^-}\frac{-(x-1)}{x-1}=-1$

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  • $\begingroup$ welcome, dear :) $\endgroup$ – R.N Sep 29 '15 at 18:53

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