Exercise 6.1.11: Fix a continuous h: [a,b] → R. Let f (x) := h(x) for x = [a,b], f(x) := h(a) for x < a and f(x) = h(b) for all x > b. First show that f: R →R is continuous. Now let fn be the function g from Exercise 5.3.7 with e = 1/n, defined on the interval [a,b]. That is, • x+1/n n fn(x): = 2 Show that {f} converges uniformly to h on [a, b]. n=1