Recent content by looserlama

Oh, I didn't think of that at all. So if I chose f(t) = t-1/3 and g(t) = t-2/3 or just f(t) = g(t) = t-1/2 Then (fg)(t) = \frac{1}{t} which is not Riemann Integrable on I = (0,1] right? Thanks so much for your guys!

Homework Statement Do the following: (a) find an interval I and functions f, g: I → R such that f and g are both Riemann integrable, but f g is not Riemann integrable. (b) find an interval I and functions f, g: I → R such that f and g are both Riemann integrable, but g ◦ f is not...

Ok. That makes sense as ln(t) increase much slower than t. So this is what I was thinking: Let f(t) = \frac{1}{ln(|t| + 1)} if t ≠ 0 and 0 if t = 0. So clearly lim as |t|→∞ of f(t) = 0, so it is in c0. But then showing it isn't in lp for every p is a bit harder. This is how I...

Homework Statement For F \in {R,C} and for an infinitie discrete time-domain T, show that lp(T;F) is a strict subspace of c0(T;F) for each p \in [1,∞). Does there exist f \in c0(T;F) such that f \notin lp(T;F) for every p \in [1,∞) Homework Equations Well we know from class that...

Ok. But if I do that won't I still get a quadratic equation relating δ and ε? So how do I get a specific δ?

Yea if it is differentiable then it's continuous. But I'm guessing I can't just state that the derivative of arctan is 1/(1 + x2). So I need to prove it. I've seen the derivation of it, using the triangle, but I don't think that's a legitimate proof is it? Wouldn't I have to use the...

Thanks, those both make sense, but I'm going to try and finish it off with the original ε,δ proof. So here's what I get: We have |x - 3| < δ and |y - 2| < δ, therefore x in (3 - δ, 3 + δ) and y in (2 - δ,2 + δ) so |x| < 3 + δ and |y| < 2 + δ hence 3|x||y| + 18 < 36 + 15δ + 3δ2 so |3xy...

Homework Statement Let zn = Arg(-1 + i/n). Find limn→∞ zn Homework Equations Definition of convergence of a sequence. The Attempt at a Solution Well zn = Arg(-1 + i/n) = arctan(-1/n). So it seems clear that limn→∞arctan(-1/n) = arctan(limn→∞ -1/n) = arctan(0) = \pi. Which is true if...

Homework Statement Let z = x + iy and let f(z) = 3xy + i(x - y2). Find limz→3 + 2i f(z). Homework Equations The definition of a limit. The Attempt at a Solution I did f(3 + 2i) = 18 - i It seems pretty clear that it is a continuous function, but I can't prove it. So I tried using the...

Oh ok, it just doesn't seem like a very formal way of showing it. Is there not a better way of doing it?

How can we have |x|^n <R if n->infinity? Wouldn't it be 1/R*limsup|x|^n <1 ? So limsup|x|^n < R and wouldn't that only be true for |x| < 1 ?

Homework Statement Suppose that the power series \sumanxn for n=0 to n=∞ has a radius of convergence R\in(0,∞). Find the radii of convergence of the series \sumanxn2 from n=0 to n=∞ and \sumanx2n.Homework Equations Radius of convergence theorem: R = 1/limsup|an|1/n is the radius of...

I'm pretty sure that's wrong, just from me computing 2n(n-1)! - \frac{n!}{n!} = 2n(n-1)! - (2n-1)(2n-3)...(3)(1) with vary large numbers. For all of them it was always positive and it was increasing as n got larger. Also, if we try dividing (2n-1)(2n-3)...(3)(1) by 2n, so dividing each term...

Yea I've been working on other stuff but I've been following the conversation. So this is where I'm at now: We've never seen stirling's approximation before so I don't think we're supposed to use it. So I've just been focusing on the Squeeze theorem way: It's easy to show...

Isn't the ratio test just for series though? Also, if we are talking about the same ratio test, then that equals 1, so it's inconclusive. That's kind of how I got to this point in my problem.