Old Test 3 with Answer Key - Numerical Analysis | MATH 375, Exams of Mathematical Methods for Numerical Analysis and Optimization

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Millersville University Name Ansyser Kea, Department of Mathematics MATH 375, Numerical Analysis, Test 3 December 07, 2006 Please answer the following questions, Your answers will be evaluated on their correctness, com- pleteness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. You may use your textbook, calculator, and notes. Un- less otherwise indicated all numerical approximations should be carried out to at least six decimal places. 1. The expected lifetime of an industrial fan when operated at the listed temperature is shown in the table below. Hrs. (1000) 40 75 50 63 60 54 (a) (12 points) Find the Lagrange interpolating polynomial of degree 3 based on the data. You do not need to simplify the polynomial completely. (x-Ha\(r- sero) |. ag (x-28-S0\(%.- G0) 2 4 Plays 9 (26- 40)(26-50)(26-60) (Wo-25)4o-Se}40- Go) (n-28r-40}hy-62) ( (e-2ske-uelx-se) (Go-28(s0-aseo-ca)] * [ [oor 25Yo- de co-so)