Question

Please make sure I'm understanding the epsilon-delta definition of a limit correctly. Intuitively, the definition is stating that no matter how narrow we choose to make the "epsilon band" surrounding f(x) = L, there will always be a "delta" band surrounding x = a that contains all the x-values that correspond to the f(x) values contained within the epsilon band. This is really just a fancy way of saying that we can take f(x) as close as we like to x = a. Am I correct?

Answer 1

http://www.maa.org/devlin/devlin_11_06.html

ed is alleged to define continuity:-)

Answer 2

Student : Car has a speed of 50? Teacher : Given any ep >0 there exists a del so that if |t2-t1| < del then |(s2-s1/t2-t1) -50| < ep