FM5002-HW10-4.18.12 (1)

2 fm5002hw1041812nb if x is at the borderlin e of two

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Unformatted text preview: e borderlin e of two bars, then f n x is the midpoint of the base of the leftmost of those two bars. a. Show that for all x b. Let g(x) = (e 2x E g D2 n , lim f n x x. n 3 . Show that 2n g fn x p n x x. a. For each n , the width of the bars of H n are 2 an d the span of H n is 2n 1 2n , 2n 2n , 1 2 n . Therefore, a fixed x must eventually lie in the span of H n , an d the value of f n x then con verges to xsince the widths of the bars decreases. b. We first evaluate the left hand side, E g D2 n 2n...
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