# Thread: Need help solving for delta part 2

1. ## Need help solving for delta part 2

I tried to mimic what the person did on the previous question but still do not understand what I am supposed to do
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→3 x^2 + 5 = 14.

2. ## Re: Need help solving for delta part 2

Originally Posted by kidgt23
I tried to mimic what the person did on the previous question but still do not understand what I am supposed to do
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→3 x^2 + 5 = 14.
To get help, please show your complete work. Otherwise, we are just guessing as to what you do not understand.

3. ## Re: Need help solving for delta part 2

so what I did was |x-2|>1 so that -1<x<-2 then 1<x<3
|(x^2+5x)-4|=|x^2+5-1|=|x-2| |x+7|
Then 1<x<3 so 4<x+7<10 Then
|x+7|<10
if epsilon>0 let Delta = min(1,Epsilon/10) So if |x-2|<Delta
(|x^2+5|-4)=|x-2| |x+7|<Delta (10) < or equal to epsilon

If this is wrong please show me the right way it is done

4. ## Re: Need help solving for delta part 2

Originally Posted by kidgt23
so what I did was |x-2|>1 so that -1<x<-2 then 1<x<3
|(x^2+5x)-4|=|x^2+5-1|=|x-2| |x+7|
Then 1<x<3 so 4<x+7<10 Then
|x+7|<10
if epsilon>0 let Delta = min(1,Epsilon/10) So if |x-2|<Delta
(|x^2+5|-4)=|x-2| |x+7|<Delta (10) < or equal to epsilon
I tried to mimic what the person did on the previous question
You did no such a thing. You did not start as I did.

$x\to 3$ $x$ approaches three so bound that: $|x-3|<1\text{ or }2<x<4$ that is step one.

Step two: we think the limit is 14 so write $|(x^2+5)-14|$, the function minus the limit.
In the case of polynomials it should factor: $|x^3-9|={\color{red}{|x-3|}}|x+3|$ there is our control.

$2<x<4\Rightarrow 5<x+3<7\Rightarrow |x+3|<7$ now you tell why all of that is done. Why +3??

If $\varepsilon>0$ then let $\delta=\min\{1,\frac{\varepsilon}{7}\}$ that forces $|(x^2+5)-14|<\varepsilon$ WHY?