(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the precise definition to show

[tex]lim (x^2+3x) = 10[/tex]

x[tex]\rightarrow[/tex]2

3. The attempt at a solution

Let [tex]\epsilon[/tex] > 0

[tex]x^2 + 3x - 10 < \epsilon [/tex]

[tex](x-2)^2 = x^2 - 4x + 4 [/tex]

This doesn't equal the equation. Add 7x, -14

[tex]\left| x-2 \right| ^2 + 7 \left| x-2 \right| [/tex]

So far it's alright. Now I need to get a value for [tex]\delta[/tex]

[tex]\epsilon[/tex] = [tex]\delta^2 + 7 \delta[/tex]

Now I'm totally confused. Normally I've used simply [tex]\delta[/tex] expressions like [tex]\delta[/tex] = [tex]\epsilon[/tex]/2. What should I say my [tex]\delta[/tex] is equal to in this case, and why?

So [tex]\left| (x^2 + 3x) -10 \right|[/tex] < [tex]\delta^2 + 7 \delta[/tex]

Any help?

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# Homework Help: Limit proof question

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