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Absolute value question

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Given: |x-a|<ε |y-b|<ε. proove: |xy-ab|<ε(|a|+|b|+ε)

    2. Relevant equations
    I need a direction for this proof.

    3. The attempt at a solution
    I tried by the info: -ε+a<x<ε+a and -ε+b<y<ε+b to ,multiply these inequalities, but it's not true. and i tried with the opposite triangle inequality and it didn't worked.
  2. jcsd
  3. Oct 29, 2012 #2


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    2017 Award

    Staff: Mentor

    You can expand |xy-ab| to contain terms like a(y-b) and then use the regular triangle inequality.
    The direction multiplication of the inequalities could work, too, but you have to be careful with signs there.
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