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# Exam2 - Department of Mathematics The exam paper for course...

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Department of Mathematics The exam paper for course 157 in June 2001. Rubric Answer three questions.

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Question 1 Express the numbers x = 12 . 74, y = 0 . 0025 and z = - 12 . 55 as three digit, decimal, floating point numbers. Compute the expression x - y x + z using three digit floating point arithmetic. Identify the rounding errors at each step of the calculation, including the representation of x , y and z , and calculate the total error due to rounding in the calculation. A sequence of estimates S i of the first derivative of f ( x ) at a point x = 1 . 5 are generated using a computer by calculating S i = f (1 . 5 + e i ) - f (1 . 5) e i with e i = 10 - i . Describe and explain the values of S i that are obtained for large values of i . Complete the following finite difference table x f Δ f Δ 2 f Δ 3 f 1 . 0 0 . 8988 625 1 . 5 0 . 9613 332 2 . 0 0 . 9945 31 2 . 5 0 . 9976 With x 0 = 1 . 0 generate a sequence of approximations for the first derivative of f at x = 1 . 5 using Newton’s Forward Formula. UA157 page 2 of 5
Question 2 Using Taylor Series, or otherwise, derive the Newton Raphson method. Use

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Exam2 - Department of Mathematics The exam paper for course...

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