Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook