Hey, I'm stuck on this problem and just wanted some help if possible.(adsbygoogle = window.adsbygoogle || []).push({});

Prove, using an [tex]\epsilon - \delta[/tex] argument, that [tex]\lim_{\substack{x\rightarrow -2}} \frac {1 - x - 2x^2} {x + 1} = 5[/tex]

Ok, so I've answered so far with:

[tex]\lim_{\substack{x\rightarrow -2}} \frac {1 - x - 2x^2} {x + 1} = 5[/tex] if [tex]\forall \epsilon > 0, \exists \delta > 0 : 0 < |x + 2| < \delta \Rightarrow |-2x - 4| < \epsilon[/tex]

Investigation to find [tex]\delta[/tex]

[tex]|-2x - 4| < \epsilon[/tex]

[tex]\Rightarrow -2|x + 2| < \epsilon[/tex]

[tex]\Rightarrow |x + 2| > -\frac {\epsilon} {2}[/tex]

Therefore, choose [tex]\delta = -\frac {\epsilon} {2}[/tex]

My problem is here, my statement was that [tex]|x + 2| < \delta[/tex], but my answer so far has given me [tex]|x + 2| > \delta[/tex]. Also, [tex]\delta[/tex] is [tex]< 0[/tex].

What should I change?

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# Homework Help: Limit proofs

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