Recent content by NickMusicMan

deluks, you are correct. The implicit function theorem implies that F=K is LOCALLY solvable for y as a function of x. That is, for each point there exists a neighbourhood of that point where y can be written as a function of x. In this case, F is only 2 variables, so "Locally solvable...

I know that for any C2 function, the mixed second-order partials are equal, and I see that this should extend inductively to a statement about the kth partials of a Ck function, but I am having trouble figuring out exactly how this works. For example, take f:ℝ2 → ℝ . fxxy=fxyy is not true...

I have tried using the triangle inequality to do so, but i haven't figured anything out yet.

I am studying for an exam, and I am trying to figure out: if you have something like e^(x^3), can you simply substitute x^3 into the M-series for e^x and get the M-series for e^(x^3)? Or would you have to cube the whole e^x series? I have encountered mixed responses to this question. This...

by the way: I totally understand intuitively why this is the case, I just figure out how to express it formally. I know that as n approaches infinity, the fraction approaches (a fixed number)/(infinity) , which means it approaches 0. How can I write this using the formal definition?

Homework Statement For a sequence a_n: If lim (a_n) =2, use the definition of a limit to show that lim (a_n / n) = 0 all limits are as n goes to infinity The Attempt at a Solution I know that I need to show: Give any \epsilon>0 there is some M so that if n>M then |a_n / n| <...

Homework Statement For what values of r does \int(from 0 to infinity) xre-x dx converge? I assume that the problem refers to r as any real number. 2. The attempt at a solution I have given this a try but I am really not confident that I did it right... First i used integration...