11:49 PM G K/S You 5 minutes ago PROGRAMME: BENG UNIVERSITY OF ABUJA FACULTY OF ENGINEERING SECOND SEMESTER EXAMINATION 3022/23 SESSION-(12 DECEMBER 2023) FEG 221-ENGINEERING MATHEMATICS I LEVEL: 200 UNITS: 3 TIME: 25 HOURS Instruction: Answer Any Five (5) questions only. All questions carry equal marks. QUESTION ONE (14 marks) For two forces a-(-31 + 2/) N and b(31+6) N acting on a body, estimate the angle between (the direction of the forces b. Find the root(s) of x-2x+5-0 QUESTION TWO (14 marks) (10 marks) (4 marks) a Using Linear Lagrange interpolation, estimate the value of log12, given that log10-1.000 and log20-1.301 b. What is the error in the estimation? (10 marks) (4 marks) QUESTION THREE (14 marks) Find the root of f(x)-x-13x+7, using 'fixed point iteration'. Choose (start from) -2.000, and stop at the fifth iteration xg (to 2 decimal places). Use the first tera (x) of the equation (f(x)), as your starting point, NOT the second term (x)! QUESTION FOUR (14 marks) a. Show the first six terms of the series: (1-x)" (4 marks) 21+ b. Using the first six terms of the series (-2)", estimate the value of (-3) c. Simplify (5 marks) (5 marks) 3+js QUESTION FIVE (14 marks) Find the root of f(x)-x-8, using the Newton-Raphson method Choose (start from) xo-1.000, and stop at x (to 2 decimal places). QUESTION SIX (14 marks) Use the Naïve Gauss elimination method to solve the following: 2x-3x+x=6 (4 니 14. 13. 5x+2x-2xy=2 = (1) (2) (3) n

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