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## Homework Statement

find an open interval about x

_{0}on which the inequality lf(x)-Ll<[tex]\epsilon[/tex] holds. Then give a value for [tex]\delta[/tex]>0 such that for all x satisfying 0<lx-x

_{o}l<[tex]\delta[/tex] the inequality lf(x)-Ll<[tex]\epsilon[/tex] holds

f(x)=x

^{2}

L=3

x

_{0}=-2

[tex]\epsilon[/tex]=0.5

## Homework Equations

## The Attempt at a Solution

0<lx+2l<[tex]\delta[/tex] [tex]\Rightarrow[/tex] lx

^{2}-4l<0.5

-0.5<x

^{2}-4<0.5

3.5<x

^{2}<4.5

[tex]\sqrt{}3.5[/tex]<x<[tex]\sqrt{}4.5[/tex]

so i thought my interval about x

_{0}would be ([tex]\sqrt{}3.5[/tex],[tex]\sqrt{}4.5[/tex]) but my book says its the negative of both those numbers, so im thinking its because x approaches -2, then my interval would be on the negative side of the x-axis?

also i dont know how my book got [tex]\delta[/tex]=[tex]\sqrt{}4.5[/tex]-2 as an answer

please help me with these limit problems, im really confused