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## Homework Statement

Suppose [itex]|f(x)-5|<0.1[/itex] when 0<x<5.

Find all values [itex]\delta>0[/itex] such that [itex]|f(x)-5|<0.1[/itex] whenever [itex]0<|x-2|<\delta[/itex]

## Homework Equations

## The Attempt at a Solution

I know that [tex]0<|x-2|<\delta[/tex]

[tex] 2-\delta<x<2+\delta[/tex]

[tex]\delta=2[/tex]

but how does this part of the equation help me find delta?

[tex]|f(x)-5|<0.1[/tex]

[tex]4.9<f(x)<5.1[/tex]

I don't undestand it's use in this problem, if the other part gave me [itex]\delta=2[/itex]