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Unformatted text preview: Answers for Review Questions for Lectures 1-4 Review Lectures 1-4 Problems Question 2. Derive a closed form for the estimate of the solution of the equation below obtained by applying 2 iterations of Newton’s Method with the initial estimate 0. Question 4. Compute the quadratic least squares . , , 2 2 π π- = x x sin 1 , |, | x x that interpolate Question 3. Compute a linear combination of functions at 2 . sin 1 . =- x x Question 1. Do problem 13 on page 79 of the textbook. approximation to the function x cos over . ] , [ 2 2 π π- Question 5. Use Gram-Schmidt to compute orthonormal functions from the sequence θ θ θ , sin , cos over . ] , [ π Question 6. Do problem 1 on page 215 of the textbook. Question 1 Do problem 13 on page 79 of the textbook. Let Find an interval [a,b] 2 ) (-- = x e x f x and for which α containing α be the largest root of the bisection method will converge to . α Then estimate The number of iterates needed to find α within an accuracy of . 10 5 8- × Answer: [a,b] = [1,2].Answer: [a,b] = [1,2]....
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