Recent content by Design

After trying this, I got a integral e-x/(x-1) which is unsolvable.

So y0 in the element of [0,1] right? and one side I got g(x) >= 0 >= g(x)-1, Is this right?

What do you mean when you mean y0 is fixed?

After you apply the IVT on g, you will get that the number between is zero?

If D is compact then f/g will be uniformly continuous on D right?

Homework Statement Assume the function f : [0,1] x [0,1] -> [0,1] is continuous and apply the IVT to prove that there is a number c E [0,1] such that f(c,y0) = c for some y0 E [0,1] The Attempt at a Solution I tried to break the cube up with the ranging being y0 but I don't know how it...

But 1 is not considering a function f is it?

I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous? I have a feeling it is not but I can't seem to find a counter example.

Homework Statement e-x/(x-1) The Attempt at a Solution I tried integration by parts and it just seems to go on endlessly and Wolfram gives some Ei function which I have no idea what it is.

Thanks, will definitely give it a shot.

Is there any other way of doing it? It just seems weird because I haven't covered anything about series solutions and all of a sudden this comes up.

Never heard of anything like this. My prof like putting problems we haven't learned in the problem set = ='. I guess its time to look it up. Don't know what you mean but y'' mutipled by (x-1)

Homework Statement y''(x-1)-xy'+y=x2-2x+1 The Attempt at a Solution I don't even know how to start this, Don't know what substitution to do.

Got it thanks.

Not sure how that would work out, only told to use t=lnx. But using y=x^{n} won't cancel the coefficients to be constants. Edit: I looked up your response on Wikipedia and found something similar on it, never learned to do it this way tho. I'll give it a shot.