Exercise 3.1.7: Find an example of a function f: [-1, 1] - R, where for A := [0, 1] we have fla (x) - 0 as x -+ 0, but the limit of f(x) as x - 0 does not exist. Note why you cannot apply Proposition 3.1.15.Proposition 3.1.15. Let S CR, c ER, and let f : S -> R be a function. Suppose A C S is such that there is some a > 0 such that (A \\ {c}) n(c-a, cta) = (S\\{c})n(c-a,cta). (i) The point c is a cluster point of A if and only if c is a cluster point of S. (ii) Supposing c is a cluster point of S, then f(x) -> Las x -> c if and only if flA(x) -> Las x -+ c