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Help with the Formal Definition (ε-δ) of limits

  1. Nov 15, 2011 #1
    Help with the Formal Definition (ε-δ) of limits!!

    Hey, I am in Honors Calc 1 in college and I have this take-home graded worksheet on Epsilon-Delta for limits and it's killing me. I have to prove that lim(x^2+3x+5)=3 as x->-2. So far I have:

    For any given epsilon>0 there is a delta such that if O<|x+2|<delta, |f(x)-3|<epsilon. (I'll use E for epsilon and D for delta)

    |x^2+3x+2|< E
    |x+2||x+1|< E

    and this is where I get stuck. I know I have to find |x+1| as a constant but I'm not sure how. I thought I should make |x+2|<D<=1, then -1<x+2<1 and -2<x+1<0, but then when I plug x+1<0 in it gives me 0|x+2|<E which doesn't make sense! Help, please! Thanks ;)

    (BTW I realized after this they have the epsilon and delta symbols on the side, sorry!)
  2. jcsd
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