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Please answer in the style of a formal proof and thoroughly reference any theorems, lemmas or...

Please answer in the style of a formal proof and thoroughly reference any theorems, lemmas or corollaries utilized.

Problem 3. (Chebyshev nodes) Let x; = - cos(ja/N), j = 0,...N. Assuming N is even, show that 21 – xo = O(1/N2) and {N/2 – XN/

Problem 3. (Chebyshev nodes) Let x; = - cos(ja/N), j = 0,...N. Assuming N is even, show that 21 – xo = O(1/N2) and {N/2 – XN/2–1 = O(1/N).
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Answer: 1 b 71-7ola 21 - Do = 1- cos using cosa a EST-CE Ě Eila za CO .. ani so lim x-xo CT² T4 Tb. N-2 /N? ca? NT #It inn Ó!

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