Recent content by kidmode01

Ah I'm all messed up now lol

Right, thanks for pointing that out. Then my integrals at the bottom of my second post change to: \lim_{n\rightarrow\infty} \int_{-1}^{-c} \phi_n(x) g(x) + \lim_{n\rightarrow\infty} \int_{c}^{1} \phi_n(x) g(x) = 0 and then as c goes to zero: 0 =...

Second attempt at solution Okay so I've tried a little bit more now: Just adding and subtracting a term from the limit we want to prove: \lim_{n\rightarrow\infty} \int_{-1}^{1} \phi_n(x) g(x)dx = \lim_{n\rightarrow\infty} \int_{-1}^{1} \phi_n(x)(g(x)-g(0))dx +...

Homework Statement Let \phi_n(x) be positive valued and continuous for all x in [-1,1] with: \lim_{n\rightarrow\infty} \int_{-1}^{1} \phi_n(x) = 1 Suppose further that \{\phi_n(x)\} converges to 0 uniformly on the intervals [-1,-c] and [-c,1] for any c > 0 Let g be any...

Haha, well thanks a lot guys :) I had thought of building it into a single ratio but I thought I was only further complicating it. Thanks again.

Okay, So I worked out the first two terms: A1 = log(1-1/4) = log(3/4) A2 = log(1-1/9) = log(8/9) then r = log(8/9) / log(3/4) But then checking A3 = log(1-1/16), A3 does not equal r*A2. So this is not a geometric series?

Homework Statement Determine the sum of the following series: \sum_{n=1}^{inf} log(1-1/(n+1)^2) Sorry for poor latex, that is supposed to say infinity. Homework Equations How might we turn this into an easier function to deal with? The Attempt at a Solution So far I've only...

I went and talked to one of my prof's about it, got it staightened out.

44 mod 4 + 44 Stop editing your post lol

It used to say "get 55..." Nice edit!

44/4 + 44. Kind of a silly question? :P [Edit] If someone can come up with something rigorous(uniqueness and existence of such numbers) good on them, I just guessed and checked.

Hello there, can someone help me with the proof? The proof in my text (Advanced Calculus, R Creighton Buck) is long and tedious and I hoped to be able to make it shorter Let O be a non empty open connected set. ---------- Aside: Then if O is broken up into Kn sets, then the intersection...

Well there is a theorem that states the image of a continuous function whose domain is a compact set is also compact but I didn't want to use any continuity for this proof. But you I know what you mean. I think for my question I can say specifcally the x_k_i's converge to x0 and the y_k_i's...

Say there is a sequence of points: { x_k,y_k } that has a convergent subsequence: { {x_k_i,y_k_i}} } that converges to: (x_0,y_0) . Sorry for poor latex, it should read "x sub k sub i" Can I extrapolate the sequence {x_k_i} and say it converges to x_0 separately? The reason I ask...

Applying the product rule first you realize you'll be using the chain rule automatically when calculating the derivatives: Take the derivative of the first term,expression,etc and multiply it by the second term. Thats the first part of your product rule. Then ADD: the derivative of the second...