Question

Precise Definition of a limit, I honestly am completely lost.

Answer 1

\[
-1 < 4x-16 < 1
\]Divide by \(4\) and \[
-\frac 14 < x-4 < \frac 14
\]Meaning \(\delta = 1/4\).

Answer 2

This doesn't hinge so much on knowing a limit, just on understanding the whole idea of what's going on in epsilon-delta proofs. So if we look at:

\[|x-4|< \delta\] \[|4x-16|< \epsilon\] we can see that we can factor out a 4 from the left side of the inequality with epsilon:

\[4|x-4|< \epsilon\]\[|x-4|< \epsilon /4\]
And now we can easily see that we can say: \[\delta = \epsilon /4\]

Answer 3

Keep in mind I said, "we CAN say," they are equal, but they don't necessarily have to be since our choice of delta can be arbitrary. I'm just trying to give a little extra perspective because I really hate epsilon delta proofs and I personally don't believe that they are capable of proving anything.

Answer 4

Luigi, is it the definition that you don't get, or these particular problem sets?

Answer 5

More of the definition.

Answer 6

Okay, I'll explain it a bit further then.

Answer 7

Explain it to us @Luigi0210 that will be the fastest way for anyone to help you.

Answer 8

I barely understand it myself .-.

Answer 9

By explain "it" I mean explain what you think a limit is, whether or not it's wrong is immaterial. Clearly you have some conception of what it is or should be.

Answer 10

Yeah, first of all, what do you think a limit is?

Answer 11

Your own embarrassment is in my opinion the worst thing that comes out of giving grades. But the point is, you don't understand it and that's precisely why you're here! To learn! We can explain how a left hand limit and right hand limit or what infinity is/might be, but overall we'd just be making large nets and hoping we get lucky.

If you show us what you think you know, we can immediately show you what's messed up to correct it as quickly as possible so you can move on to bigger and better things.