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(2) (10 marks) On the space C([0, 1]) equipped with the usual sup-norm || ||, consider the sequence of functionals (ln)neN given by p1 lu(f) = n [/" f(x) dx. Prove that this sequence converges weakly and find its limit. Is it convergent in norm? (2) (10 marks) On the space C([0, 1]) equipped with the usual sup-norm || ||, consider the sequence of functionals (ln)neN given by p1 lu(f) = n [/" f(x) dx. Prove that this sequence converges weakly and find its limit. Is it convergent in norm