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I'm trying to use the epsilon delta definition to prove that $$\lim _{x\to-2} (2x^2+5x+3)=1$$

evaluating: $|(2x^2+5x+3)-1|\lt \epsilon$

under the condition: $0\lt |x-(-2)|\lt\delta$

I arrived at: $|((x+2)+(x+2)-3)(x+2)|\lt \epsilon$; which simplifies to: $(2\delta-3)(\delta)<\epsilon$

What to do now? Do I evaluate the prior expression so as to get an appropriate range and relation between epsilon/ delta, upon which the limit is condition. If so how?

btw, this question makes use of a similar previous question Use the epsilon-delta definition to prove the following statement.

Thanks

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    See [here](http://math.stackexchange.com/questions/209440/how-to-show-that-fx-x2-is-continuous-at-x-1/209492#209492).2012-10-15

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