Recent content by mathgeek4

The answer is (0,-12). All you really know here is that (6,-12) lies on y=f(x), but you do not know what is f(-x/3+6)=?. So you can only use the given info. And I think the explanation given by SammyS is the best way to do this.

your attempt at the solution seems right to me.. as long as the variable i does not depend on t.. There are two errors (i) you have changed the minus sign from the original Integral to a + sign when you are actually evaluating it. and when you plug the limits -1 and 1, you should get...

can you show me how you get 1/2p? Because I was kind of getting to the same thing at one point.

The answer was given in the book as 1/(1+p). In the general case, did u look at the distance between 1/n^p and 1/(n+1)^p?

I think the rest of the would be negligible as n increases. But this way I don't get the correct answer which should be 1/3. This problem has completely consumed me, it get so complicated when u start using the distance between 1/n^p and 1/(n+1)^p. Do u think I can generalized on similar lines...

btw the answer for the general case is 1/(1+p).

I understand what you did here. So working on th same lines I tried to generalize it for p=2. If we take the distance between 1/n^2 and 1/(n+1)^2 then it is greater than 1/(n+1)^4. So now if choose this value to be my epsilon, I need atleast n intervals to cover the points 1,1/4,1/9...

I understand what you did here. So working on th same lines I tried to generalize it for p=2. If we take the distance between 1/n^2 and 1/(n+1)^2 then it is greater than 1/(n+1)^4. So now if choose this value to be my epsilon, I need atleast n intervals to cover the points 1,1/4,1/9...

Thanks a lot for your help. I will go through the solution that you gave here tonight, and will get back to you tomorrow. The real challenge is to generalize it for any p. I appreciate your time. Thanks.

Box counting dimension! please help! Hi all, I am working on a problem from Chaos theory, I have to find the box counting dimension of the set {0}U{n^-p} where n is an integer and p>0. I started this problem by considering p=1. So, the set looks like {0,1,1/2,1/3,...}. If I take intervals...