Recent content by wackikat

I've tried using Cauchy, but I just seem to end back with a term I started with. Here's what I tried. |f_n(x) -f_m(x)| = |f_n(x) + f_n(y) + f_n(y) - f_m(x)| <= |f_n(x) + f_n(y)| + |f_n(y) - f_m(x)| <= C|x-y| + |f_n(y) - f_m(x)| = C|x-y| + |f_n(y) -f_n(x) + f_n(x) - f_m(x)| <= 2C|x-y| +...

Homework Statement Let f_n be a sequence of function whcih converges pointwise on [0,1] where each one is Lipschitz with the same constant C. Prove that the sequence converges uniformly. Homework Equations A function is called Lipschitz with Lipschitz constant C if |f(x)-f(y)| <= C|x-y|...

I would assume that Lazorlike meant that |f'(c0)| > f(0) which is true since f(0)=0 and absolute value has to be positive, but it's not what we need to show. -------I see you've alreay explained this. I understand how you interpreted the problem--if only life were that easy.

I don't see how this creates a contradiction. We need |f '(c0)| > |f (c0)|

I figured it must be something really simple. For some reason I seem to do better with the difficult ones. I can convince myself that f(x) must equal zero in order for the inquality to hold but still can't grasp how to actually prove it. I have a page full of scratch work trying to use the...

Thanks for trying lurflurf, but I have no idea what you are trying to do.

Opps what I meant to say was that I was wondering if there was a way to to show f'(x)=0 which would imply f is constant

Homework Statement Suppose that f:R->R is differentiable, f(0)=0, and |f'(x)|<=|f(x)| for all x. Show that f(x)=0 for all x Homework Equations f'(a) = limit as x->a [f(x) - f(a)]/[x-a] The Attempt at a Solution I feel like this should be something simple, but I don't know how to...