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Let Ra be equipped with the Euclidean norm, let DCR be a closed set, let g: D-D be a contraction with Lipschitz constant L=1/3, let XOED and assume that DcB2(Xo). By the contraction mapping principle, there exists a fixed point x ED of g, and the sequence (XK)k generated by the iteration Xk+1 = 8(Xk) fork EN converges to x*. What is the smallest number NEN such that for any dimension de1, and for any D, g and xo as characterised above, we have iNZYA (*X ) 8-0'g = 4x Hint: You can derive a lower bound BEN on N by considering concrete examples. To derive an upper bound NsB+ on N, you have to write down a short mathematical argument. If you manage to match B.=B+, the statement B.sNsB+ becomes B.=N=P+. You have identified N. O a. N=0 O b. N=1 O c. N=2 O d. N=3 O e. N=4 Of. N=5 O g. N=6 Oh. N= 12 Oi. N=18 O j. N=54 O k. N=129140163