Let Prove that (a) if exists, then sup (A) = inf {u: u is an upper bound of A}.(b) if exists, then inf (A) = sup{l: l is a lower bound of A}.

Consolidated Calculus Chapter 2 Notes Limits: As function f(x) approaches a number “a” but does not touch at that value, we get Where “a” is a value of x, f(x) is the function and ” is the value of the limit. One sided Limits: Limit as x approaches a from the left, as Limit as x approaches a from the right Noted by the minus sign attached to a as noted by the plus sign attached to a The rational function 1/x^2 has a limit that looks like this: The limit is equal to infinity because on both sides of x=0 the function approaches but never touches the line of x=0. Instead the function continues to infinity. This is known as a vertical asymptote. For a vertical asymptote to exist: Which for this this to be tru