1. Consider the following table. xi 4.0 4.2 4.5 4.7 5.1 5.5 5.9 195.14 224.87 6.3 256.73 Y₁ 102.56 113.18 130.1178 142.05 167.53 a) Construct the least squares polynomial of degree 4 and compute the error. b) Construct the least squares approximation of the form be ax, and compute the error.
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- Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2, (A1 × A2) × A3, A1 × A2 × A3.Q_5 Suppose f:RZ where fx=2x-1.If A={x |1x 4}, find f(A).If B={3,4,5,6,7}, find f(B).If C={-9, -8}, find f^ - 1(C)The factorial function f(n) = n! is defined by n! = 1 2 3... n whenever n is a positive integer, and O! = 1. Provide big-O estimates for the factorial function and the logarithm of the factorial function. As an illustration, 1! = 1, 2! = 1 2=2, 3! = 1 23 = 6, and 4! = 1 234=24.Take note of how quickly the function n! expands. Consider the following: 20! = 2,432,902,008,176,640,000.
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- Given X = {1, 2, 5, 8, 9}, Y = {3, 4, 6, 7, 8}, Z = {1, 2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Findthe following: 1. (X -Z̅) ∪ Y2. (X̅ ∪ Z) ∩ Y3. (Y ∩̅Z) ∩ X4. (X ∩ Z) - (X ∪ Y)5. Z̅ – (Y ∩ X)Let A = {c, n, b}, B = {x, y} and C = {0, 1}. Find A)A X B X C B)C X B X A C)B X C X CGiven A={1,2,3,4,5,6},B={4,5,6,7,8,9}. Compute (e)B⊕A= (f) (A−B)∩(B−A) =