Question

http://gyazo.com/97dbcc6c159b083ec68c157711474f71 Number 11

Answer 1

Print too small to read.

Answer 2

@aum is this better http://gyazo.com/1f068513c3fe8f37f1a54ef71120304d.png

Answer 3

|f(x) - 6| < 3 implies:
-3 < f(x) - 6 < 3
add 6 throughout
3 < f(x) < 9
Read the graph to see when f(x) = 3 and f(x) = 9. f(1) = 3 and f(5) = 9
f(1) < f(x) < f(5)

Therefore, the maximum delta can be is 5 - 3 = 2. (or 3 - 1 = 2)

Answer 4

Oo ok :)

Answer 5

Follow the same procedure for part 2.

Answer 6

It saying the answer for b is 1/2 ?

Answer 7

correct. Do you need the steps?

Answer 8

Yes so I can see it out

Answer 9

Please :)

Answer 10

@aum

Answer 11

@e.mccormick

Answer 12

It is simply following the same steps but starting with < 1 rather than < 3.

Answer 13

Ok so if i do that I get -1<f(x)-6<1
Then I get 5<f(x)<7
But don't get 1/2 as the answer

Answer 14

Did you look at the f(x) for those values?

Answer 15

F(2 1/2) = 5

Answer 16

And f(3 1/2) = 7 id what I get

Answer 17

Yes. We are taking the limit as x approaches 3.
So the maximum we can go from 3 is: +1/2 or -1/2

So maximum |delta| = 1/2

Answer 18

Oooo. Ok :)

Answer 19

Yah, you are looking at how far the input values are from the center value. So because you are looking at \(x\rightarrow 3\) you need to look at how far each of those are from 3. That is where the \(\pm \dfrac{1}{2}\) comes in.

Answer 20

3 + 1/2 = 3.5
3 - 1/2 = 2.5

And those are the domain values you found for that epsilon range.

Answer 21

Thanks for both for the help

Answer 22

You are welcome.

Answer 23

I tried to map your function to help with the meaning of \(\epsilon - \delta\), but did not quite get it.

https://www.desmos.com/calculator/qbqhmrz3mb

What this whole thing is about is the input, \( \delta\), and it's relationship to the output, \( \epsilon\), when you are looking for something that is "close enough."

Lets say you don't know the answer and can't easily calculate it. But, you want to get within \( \epsilon\) of the correct answer. With this process you can find the \( \delta\) that will get you there.

Now, not all functions are nice and ballanced so the \(\pm\) will be the same on both sides. In those cases, take the smaller \( \delta\) distance. The reason why is because the larger would be incorect for one of the answers, but the smaller is correct for both.