Select ALL of the following statements which are NOT correct. Let fn (x) . , and...

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Select ALL of the following statements which are NOT correct. Let fn (x) . , and x E R, such that {fn } || 1+na? n = 1, 2, 3, . ... converges uniformly to a function f. Then f' (x) = limn In (x), for any x E R. Assume {fn}, {gn} are defined on E. and fn uniformly bounded partial sums, and In converges uniformly to ) on E. Then fn9n converges uniformly on E. (Hint: "uniformly bounded partial sum" means there exists M > 0, s.t. E-1 fn < M for any N) x2, -x², if x < 0. such that f (x) = Eanx", for x E (-1, 1). if x > 0, Let f(x) : = { Then there exists a power series > an x" O Let { fn} be a sequence of continuous functions defined on a set E, if lim, Xn > x, and x E E. Then {fn} converges uniformly to f on E. fn (xn) = f (x) for every sequence of points xn E E such that Select ALL of the following statements which are NOT correct. Let fn (x) . , and x E R, such that {fn } || 1+na? n = 1, 2, 3, . ... converges uniformly to a function f. Then f' (x) = limn In (x), for any x E R. Assume {fn}, {gn} are defined on E. and fn uniformly bounded partial sums, and In converges uniformly to ) on E. Then fn9n converges uniformly on E. (Hint: "uniformly bounded partial sum" means there exists M > 0, s.t. E-1 fn < M for any N) x2, -x², if x < 0. such that f (x) = Eanx", for x E (-1, 1). if x > 0, Let f(x) : = { Then there exists a power series > an x" O Let { fn} be a sequence of continuous functions defined on a set E, if lim, Xn > x, and x E E. Then {fn} converges uniformly to f on E. fn (xn) = f (x) for every sequence of points xn E E such that