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VIDEO ANSWER Define f n 0 1 rightarrow mathbf R by the equation f n x x n Show that the sequence left f n x right converges for each x in 0 1 but that the sequence

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VIDEO ANSWER A discontinuous limit of continuous functions For each integer n and 1

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VIDEO ANSWER Okay so in this exercise we have our sequence of functions fn of x equal to x to the n Well we claim that fn does not converge pointwise on R

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The process involves orthogonalizing a set of linearly independent vectors in this case polynomials to obtain a set of orthogonal vectors

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