Find an explicit example of a sequence of differentiable functions on [−1,1] that converge uniformly to a function f such that f is not differentiable. Hint: There are many possibilities, simplest is perhaps to combine ∣x∣ and 2nx2+2n1, another is to consider x2+(1/n)2. Show that these functions are differentiable, converge uniformly, and then show that the limit is not differentiable.