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Now if you take |2/3x||x-1/2| < A why do we bound |2/3x| and not |3x/2| ?

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- #1

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Now if you take |2/3x||x-1/2| < A why do we bound |2/3x| and not |3x/2| ?

- #2

HallsofIvy

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As for |2/(3x)||x- 1/2|< A, that is the same as |x- 1/2|< A/|2/(3x)|. Comparing with you inequality above, yes, the thing corresponding to |x+3| is |2/(3x)|. Why would you think it would be |3x/2|?

- #3

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0<|x-(1/2)|<B implies |f(x)-L|<A

If we arrive at

|2/3x||x-(1/2)| < A, I thought we could just write this as |x-(1/2)| < A |3x/2|

and not worry about bounding anything coz theres no chance of getting a zero on the bottom line of the right hand side

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