Express the following as an Epsilon-Delta proof (to show that it is continuous):

Can someone give me ideas for this one?

Printable View

- November 23rd 2006, 05:46 PMJacobpm64Epsilon-Delta
Express the following as an Epsilon-Delta proof (to show that it is continuous):

Can someone give me ideas for this one? - November 23rd 2006, 06:08 PMThePerfectHacker
- November 23rd 2006, 06:40 PMJacobpm64
all right, I understand where you got the x < N, because x doesn't approach a specific value, but it does have to be less than some number N.

So, usually I'd write

Then I'd try to get that in the form

How do I do that here? - November 23rd 2006, 06:50 PMThePerfectHacker
- November 23rd 2006, 06:54 PMJacobpm64
Oh, all right.. No delta because x is extending without bound towards negative infinity, but there is an epsilon because the function approaches a finite value of L, correct?

I understand that.

But, I still don't know how I'd go about constructing a proof. - November 23rd 2006, 07:05 PMThePerfectHacker
Say you want to show,

You need to show that for any

We can choose an

Such that if,

is in the domain of the function.

Implies,

Since both side are positive we can take the reciprocal of both sides, but then we have to flip the inequality, obtaining an equivalent statement,

That means, .

We also note that,

is in the domain of .

So this tell us given any we need to choose - November 23rd 2006, 07:24 PMJacobpm64
wow, major headache.. I understand all your examples

Thing is. The only thing that's killing me on mine is that there is no specific function... I'm just given f(x)

In your example, you wrote

as

That isn't too bad to do because f(x) is defined as a specific function,

I don't know how I'd write in the form x < something, when I don't have any specific function, so I only have an f(x), not an x.

*sigh*