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Unformatted text preview: University of California, Berkeley College of Engineering Fall Semester 2009 Professors R. Horowitz and A. Packard E7 Midterm Examination II Friday November 20, 2009 Name : SID : Section: 1 2 (Please circle your lecture section) Please mark your Laboratory section: (where your exam will be returned) / 11: TuTh 810 (1109 Etch) / 12: TuTh 1012 (1109 Etch) / 13: TuTh 122 (1109 Etch) / 14: TuTh 24 (1109 Etch) / 15: TuTh 46 (1109 Etch) / 16: MW 810 (1109 Etch) / 17: MW 1012 (1109 Etch) / 18: MW 24 (1109 Etch) / 19: MW 46 (1109 Etch) / 20: MW 24 (2109 Etch) / 21: TuTh 1012 (212 Wheeler) / 22: TuTh 122 (2109 Etch) / 23: TuTh 810 (212 Wheeler) / 24: MW 35 (212 Wheeler) Part Points Grade 1 12 2 10 3 20 4 16 5 12 6 18 7 12 TOTAL 100 1. Write your name on each page. 2. Record your answers ONLY on the spaces provided. 3. You may not ask questions during the examination nor leave the room before the exam ends. 4. Close book exam. Two 8 . 5 ” × 11 ” sheets of handwritten notes allowed. 5. No calculators or cell phones allowed. (Please turn cell phones off) E7 Midterm II, Fall 2009 NAME: 1. The graph of the polynomial function f ( x ) = x 3 2 x 2 2 x + 3 is shown below. Its derivative is d dx f ( x ) = 3 x 2 4 x 2 .21.510.5 0.5 1 1.5 2 2.5 3108642 2 4 6 x f(x) (a) Assume that you are using the bisection algorithm to find a root of f ( x ) and that the initial search interval is [ x L ,x R ] = [ 2 , 3] . In the space provided below write down the value of the root that the algorithm will find, by reading its approximate value from the graph 1 . Ans: (b) Assume that you are using the NewtonRaphson algorithm and that the initial root estimate is x = 0 . Compute numerically (not graphically) the value for x 1 , the root estimate after the first iteration of the algorithm is completed. x 1 = (c) Write down the value of the root that the NewtonRaphson algorithm will find, if the initial root estimate is x = 2 , by reading its approximate value from the graph. Ans: 1 Write your answer with only two significant figures, e.g. 2.3, when reading values from the graph. page 2/10 E7 Midterm II, Fall 2009 NAME: 2. Let x 1 , x 2 , x 3 , and x 4 be the unknown test scores of the four students Erin, Tina, Jack and Ben respectively and denote the vector x as x = x 1 x 2 x 3 x 4 where x 1 represents Erin s Score x 2 represents Tina s Score x 3 represents Jack s Score x 4 represents Ben s Score ....
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 Fall '08
 Patzek
 Polynomials, Least Squares, Regression Analysis, data points, Cubic function

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