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Unformatted text preview: Math 174/274 Midterm January 28, 2009 • Please put your name, ID number, and sign and date. • There are 4 problems worth a total of 100 points. • Calculators are allowed but you must show your work to receive credit . Print Name: Student ID: Signature and Date: Problem Score 1 /25 2 /25 3 /25 4 /25 Total /100 1 1. (25 pts) Circle the best answer for the following multiple choice problems (you do not need to show work): (i) M¨uller’s method will converge to a root in one step for which of the following functions (regardless of initial guesses)? (a) x 3 (b) x 2 + 1 (c) 3 x- 2 (d) all of the above (ii) Newton’s method may not exhibit second order convergence to the root x = 2 for which of the following functions (even when x is taken arbitrarily close to the root)? (a) x 2- 2 x x + 1 (b) braceleftBigg e x − 2- 1 , x ≥ 2 x- 2 , x < 2 (c) x 2 ( x- 2) (d) none of the above (iii) Which of the following is false about the Bisection method when applied to a continuous function f (...
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- Spring '08
- Math, initial guess, Root-finding algorithm, following multiple choice, approximations