Formal Definition of a Limit Example 2

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Why 2|x-2|<epsilon???. I've already watched many videos of this definition and i still don't understand this part

ronicesarrc
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The other comments are right....I teach this and even I am confused after step three. You should have shown the correct bounding by use of laws of strict inequalities and absolute value. The 1<x<3 leading to the "=2" part is misleading and is not the true analysis in advanced calculus.

matrixate
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Yeah, this was not a good explanation, sorry

tk