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6 equip v c01 with the l2inner product 61 determine...

Question: 6 equip v c01 with the l2inner product 61 determine...

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$6- Equip V C(0,1) with the L2-inner product. 6-1) Determine the best approximation to f (x) by a polynomial of degree at most 1. Use {1,x^ as a basis for Pi. 6-2) Prove that ,x-is an orthogonal set in V. Use the fact that dimP-2 and the result of Exercise 5 to explain why this set is a basis for P 6-3) Determine the best approximation to f(x)-ex by a polynomial of degree at most l. Use the orthogonal set(i,x-j as a basis for Pi$

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