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a3_09s

a3_09s - DALHOUSIE UNIVERSITY(Department of Engineering...

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DALHOUSIE UNIVERSITY (Department of Engineering Mathematics) ENGM-3052 Numerical Methods and Linear Algebra ASSIGNMENT #3 DUE: OCTOBER 13, 2009 1. Consider the data below. x ) ( x f 1.1 9.025013 1.2 11.02318 1.3 13.46374 1.4 16.44465 (a) Derive the most accurate formula (assuming only these point have been given) from the Taylor Series and then calculate the value for ) 1 . 1 ( f (b) Derive the most accurate formula from the Taylor Series and then calculate the value for ) 3 . 1 ( f 2. Use the bisection method to find a real root between the brackets LB = 1, RB = 2 of the polynomial ) 3 / 2 sin( ) ( 2 x x x f + = . Calculate how many iterations are required so that the last two midpoints are within 0.1 of each other. Find the approximate root to within 0.1. 3. Use a two-point central-difference formula and a two-point forward difference formula to calculate ) 6 . 0 ( f where 2 ) ( - = x e x f x accurate to 12 decimal places. Begin with

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a3_09s - DALHOUSIE UNIVERSITY(Department of Engineering...

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