- #1
miglo
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Homework Statement
find an open interval about x0 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-xol<[tex]\delta[/tex] the inequality lf(x)-Ll<[tex]\epsilon[/tex] holds
f(x)=x2
L=3
x0=-2
[tex]\epsilon[/tex]=0.5
Homework Equations
The Attempt at a Solution
0<lx+2l<[tex]\delta[/tex] [tex]\Rightarrow[/tex] lx2-4l<0.5
-0.5<x2-4<0.5
3.5<x2<4.5
[tex]\sqrt{}3.5[/tex]<x<[tex]\sqrt{}4.5[/tex]
so i thought my interval about x0 would be ([tex]\sqrt{}3.5[/tex],[tex]\sqrt{}4.5[/tex]) but my book says its the negative of both those numbers, so I am thinking its because x approaches -2, then my interval would be on the negative side of the x-axis?
also i don't know how my book got [tex]\delta[/tex]=[tex]\sqrt{}4.5[/tex]-2 as an answer
please help me with these limit problems, I am really confused