2. Let {fn(x)} be a sequence of real-valued functions on [a, b]. Suppose that {fn} is uniformly Cauchy, which means: for any e > 0, there exists so that n, m > N |fn(x) – fm(x)| < e for all x E [a, b] Show that fn converges uniformly, which means that there exists a function f on [a, b] so that for any e > 0, there exists N so that 1f. (21) – f(z)| < e for all ze (a, 6) x E [a, b] n > N →

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