# Thread: Need help solving for delta

1. ## 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.

2. ## Re: Need help solving for delta

Originally Posted by kidgt23
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 $|(x^2+5x-2)-12|=|x-2|\cdot|x+7|<\delta\cdot 10\le \varepsilon$.