Proving |xy-ab| is Less Than Epsilon: Absolute Value Question | Homework Help"

[mercuryman]

Homework Statement

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

Homework Equations

I need a direction for this proof.

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.

 

[mfb]

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.