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Thread: Need help solving for delta

  1. #1
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    Need help solving for delta

    I really do not know what to do with this questions I have tried factoring and solving for the limit but still cant find delta
    Find a δ for which the following statement is true. Start by stating the definition of the limit as applied to this question: lim x→2 x^2 + 5x−2 = 12.
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  2. #2
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    Re: Need help solving for delta

    Quote Originally Posted by kidgt23 View Post
    I really do not know what to do with this questions I have tried factoring and solving for the limit but still cant find delta
    Find a δ for which the following statement is true. Start by stating the definition of the limit as applied to this question: lim x→2 x^2 + 5x−2 = 12.
    First, step one say $|x-2|<1$ so that $-1<x-2<1$ means that $1<x<3$. Now we know the bounds on $x$.

    Next: $|(x^2+5x-2)-12|=|x^2+5x-14|=|x-2|\cdot|x+7|$ and there it is the term $|x-2|$, the one we control.

    From the first step $1<x<3$ so $4<x+7<10$ which implies $|x+7|<10$ Now both terms are bounded.

    It $\varepsilon > 0$ let $\delta=\text{min}\{1,\frac{\varepsilon}{10}\}$

    So if $|x-2|<\delta$ we have the bounds so that $|(x^2+5x-2)-12|=|x-2|\cdot|x+7|<\delta\cdot 10\le \varepsilon$.
    Thanks from kidgt23
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