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EGR_102_Lecture_08_HW_Solution-1

# EGR_102_Lecture_08_HW_Solution-1 - b Using 5 iterations of...

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EGR 102 of 2 pages Lecture 08 HW 1 EGR 102 Lecture 08 HW Due at beginning of lecture on Friday, March 16 2 Problems, 20 Points Total Name: Solution PID: Lab Section #: Problem 1 (12 pts): Determine the roots of the equation: ƒ( x ) = –0.5 x 2 + 2.5 x + 4.5. a. Graphically using MATLAB to show all possible roots. b. Using the quadratic formula. c. Using 3 iterations of the bisection method to determine the highest root. Employ initial guesses of x l = 5 and x u = 10. Use 3 decimal places. (a) A plot indicates that roots occur at about x = –1.4 and 6.4. (b) 40512 . 6 40512 . 1 ) 5 . 0 ( 2 ) 5 . 4 )( 5 . 0 ( 4 ) 5 . 2 ( 5 . 2 2 x (c) First iteration: 5 . 7 2 10 5 r x 9375 . 21 ) 875 . 4 ( 5 . 4 ) 5 . 7 ( ) 5 ( f f Therefore, the bracket is x l = 5 and x u = 7.5. Second iteration: 25 . 6 2 5 . 7 5 r x 672 . 2 ) 59375 . 0 ( 5 . 4 ) 25 . 6 ( ) 5 ( f f Consequently, the new bracket is x l = 6.25 and x u = 7.5. Third iteration: 875 . 6 2 5 . 7 25 . 6 r x -8 -4 0 4 8 -5 0 5 10

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EGR 102 of 2 pages Lecture 08 HW 2 Problem 2 (8 pts): Determine the roots of the equation: ƒ( x ) = 5 x 3 – 5 x 2 + 6 x – 2. a. Graphically using MATLAB to show all possible roots.
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Unformatted text preview: b. Using 5 iterations of the bisection method to determine the highest root. Employ initial guesses of x l = 0 and x u = 1. Use 5 decimal places. (a) A plot indicates that a single real root occurs at about x = 0.42. (b) First iteration: 5 . 2 1 r x 75 . ) 375 . ( 2 ) 5 . ( ) ( f f Therefore, the new bracket is x l = 0 and x u = 0.5. The process is then repeated and after 5 iterations yielding a root estimate of 0.40625. iteration x l x u x r f ( x l ) f ( x r ) f ( x l ) f ( x r ) 1 0.00000 1.00000 0.50000 -2.00000 0.37500 -0.75000 2 0.00000 0.50000 0.25000 -2.00000 -0.73438 1.46875 3 0.25000 0.50000 0.37500 -0.73438 -0.18945 0.13913 4 0.37500 0.50000 0.43750 -0.18945 0.08667 -0.01642 5 0.37500 0.43750 0.40625 -0.18945 -0.05246 0.00994 -8-4 4 8-1 1...
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EGR_102_Lecture_08_HW_Solution-1 - b Using 5 iterations of...

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