Are the following statements true or false? If true give a proof, and if false give a counter-example: (a) Assume that that a sequence of continuous functions fn converges uniformly to a function f on the interval (a, b). This means that: ∀ε>0 ∃N>0 ∀n>N ∀x∈[a,b] :  |fn(x)−f(x)|<ε. Then the function f is also continuous. (b)Assume that that a sequence of differentiable functions fn converges uniformly to a function f on the interval (a, b). Then the function f is also differentiable

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