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chapsticks
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Homework Statement
use the elipson-delta of a limit to justify the answer of: show proof
lim x->0 1/(x+1)
Homework Equations
lim x->0 1/(x+1)=1
The Attempt at a Solution
lim x->0 1/(x+1)I did some work but after that I don't know how to keep going.
if 0<|x-c|<δ => |f(x)-<ε|, then lim x->c f(x)=L
0<|x-0|<δ=> |1/(x+1)-1|
scratchwork: |1/(x+1)-1|<ε
|x/x+1|<ε
|x|/|x+1|<ε
|x|<|x+1|ε
restrict |x|<1/2
-1/2<x<1/2=>1/2<x+1<3/2=>1/2 <|x+1|
|x|<|x+1|ε
|x|<1/2 ε
δ=min{1/2,1/2ε}
how do I find the proof ??