Recent content by MarlyK

Thanks - I was having trouble trying to find a way to imagine picking a larger epsilon while keeping it arbitrarily close to zero, but I see now that if we define the relation as a proportion of the smaller epsilon, this works. Thanks.

Homework Statement I'm wondering why we can't use less than or equal to for the formal definition of the limit of a function: Homework Equations lim x→y f(x)=L iff For all ε>0 exists δ>0 such that abs(x-y)<δ implies abs(f(x) - L)<ε Why not: lim x→y f(x)=L iff For all ε>0 exists...

What I really mean to ask is let's take all linear paths - i.e. with a function f:R^2->R take the limit along y=cx or x=cy for all values c, and if all these values converge to the same limit for which the function is defined, f(a,b), why doesn't that prove continuity at that point? To try...

I know its a pretty elementary question, but I never felt like I've had any sort of reasonable explanation of why. As I understand, we can define continuity for a function f: ℝn→ℝ as: For any ε>0 there exists a δ>0 such that for all x st 0< lx - al < δ then lf(x) - f(a)l < ε Alright, so...

Hey - I think if you define continuity to be: For any positive number ε>0 there exists a δ>0 such that for l x - a l < δ → l f(x) - f(a) l < ε You are correct. But that's only provided we don't restrict i x - a l from being greater than zero, which is what I've most often come across.

Hey - I would also be interested. I haven't worked with online study groups before though. I've got about the same background as Dr. Seafood - have taken a multivariable calculus course and now taking a calculus course in R^n that covers most of the topics he has listed. Not sure what pace...