final_sol

# final_sol - CE 335 Final Exam Solutions 1] For the branch...

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CE 335 Final Exam Solutions 1] For the branch of the tangent function between -π/2 and π/2, the root is at x = 0. The smallest positive root is found on the next branch, in the positive half where π < x < 3π /2 -- in fact, we need that tan( x ) ~ 4. Taking (after some exploration) as our starting point x = 4.5, x tan( x )- x tan'( x )-1 correction (f( x )/f'( x )) 4.5 0.13733 21.505 0.0063861 4.4936 0.0041319 20.230 2.0425e-04 4.4934 which, judging by the size and rate of shrinking of the corrections, is accurate to within 10 -4 . 2] (a) The normal equations are X T Xd = X T x , where X has as its first column the squares of the t -values, the t -values as its second column, and ones in its third column, x is a vector of the x -values, and d is a vector of the unknown coefficients a , b , c . This works out to [15664 1800 20; 1800 220 30; 220 30 6] for X T X , and [2164; 226; 29] for X T x . (b) Using Gaussian elimination, we get [0.49; -3.71; 5.54] for the least-squares estimate

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## This note was uploaded on 08/30/2011 for the course CGN 3350 taught by Professor Lybas during the Spring '11 term at University of Florida.

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final_sol - CE 335 Final Exam Solutions 1] For the branch...

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