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

[NWeid1]

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!)

 

[lippyka]

Here's a hint: since |x+1| is always non-negative, you can simplify the inequality to |x+2|<D<=1 and then solve for D. In other words, if |x+2|<D, then |x+1| must be less than or equal to 1. This will give you a definite value for delta that satisfies the inequality.