Recent content by Trung

I feel embarassed for asking, but is there a fast way to calculate this without using integration by parts? \int 2e^(-2x)x^-1dx, 0 <= x < infinity There's supposed to be some kind of trick, right?

Pictorially it would be something like this: <---------------(---x---)---------(-----y-----)---------------> ...but this diagram does not constitute a proof. I do not know how to make it into a rigorous argument. I have the sets (x-r, x+r) and (y-s, y+s) but I don't know what to do with...

Homework Statement Let x and y be real numbers. Prove there is a neighborhood P of x and a neighborhood Q of y such that P intersection Q is the empty set. Homework Equations The Attempt at a Solution Sorry, I know this is elementary to many of you, but I am just starting out...

Homework Statement Find all functions v(x,y) such that both v_x(x,y) = x^2 + y and v_y(x,y) = x - y^3. Homework Equations The Attempt at a Solution I have no idea how to start. My instructor says to guess the solution, which I have tried, but failed.