So i did absolute(f(x)-f(y))= abs( ((x^2)/((x^2)+1)) - ((y^2)/((y^2)+1)) ). I simplified this to get abs( ((x^2)-(y^2))/((x^2)+1)((y^2)+1)) ).
Now I tried to set it up so that abs ( x-y ) is less than 1 (which would be one of the minimum components of delta) so that I can try to...
Hey, so one of the problem I had was that I could not find a way to show it was continuous. I tried to show it using the delta-epsilon definition of continuity, but couldn't figure out a way to find delta.
Can a function f: (a,b) in R be bounded and diffferentiablle, but have an unbounded derivative. I believe it can, but can not think of any examples where this is true. Anyone have any ideas?
Question: Suppose that f(x)>0 on (0,1) and that lim as x goes to 0 exists for the function. Show that lim as x goes to 0 for the function is greater than or equal to 0.
So I know that intuitively that this is true for obvious reasons, but I can not think of a clever way to set up the proof...
Question: Show that f(x)= (x^2)/((x^2)+1) is continuous on [0,infinity). Is it uniformly continuous?
My attempt: So I know that continuity is defined as
"given any Epsilon, and for all x contained in A, there exists delta >0 such that if y is contained in A and abs(y-x)<delta, then...