UNIVERSITY OF ABUJA FACULTY OF ENGINEERING ري PROGRAMME: B.ENG SECOND SEMESTER EXAMINATION 2022/23 SESSION - (12 DECEMBER 2023 FEG 221-ENGINEERING MATHEMATICS II LEVEL: 200 UNITS: 3 TIME: 2.5 HOURS Instruction: Answer Any Five (5) questions only. All questions carry equal marks. QUESTION-ONE (14 marks) a. For two forces a=(-31+2) N and 5 = (3i+6) N acting on a body, estimate the angle between (the direction of) the forces b. Find the root(s) of x²-2x+5=0 (10 marks) (4 marks) QUESTION TWO (14 marks) a. Using Linear Lagrange interpolation, estimate the value of lo, 12. given that log10-1.000 and log20 1.301 (10 marks) (4 marks) b. What is the error in the estimation? QUESTION THREE (14 marks) Find the root of f(x) = x²-13x + 7, using 'fixed point iteration. Choose (start from) x = 2.000, and stop at the fifth iteration xs (to 2 decimal places). Use the first term (x2) of the equation (f(x)), as your starting point, NOT the second term (x)! QUESTION FOUR (14 marks) 2. Show the first six terms of the serius: (1x)" (4 marks) b. Using the first six terms of the series (1-x)". estimate the value of (-3)5 21+1 c. Simplify (5 marks) (5 marks) 3+15 QUESTION FIVE (14 marks) Find the root of f(x)=x³-8, 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 Gaus: climination method to solve the following: x1+5x2+x3=12 2x-3x2+x=6 5x,+2x2-2x=2 (1) (2) (3)
UNIVERSITY OF ABUJA FACULTY OF ENGINEERING ري PROGRAMME: B.ENG SECOND SEMESTER EXAMINATION 2022/23 SESSION - (12 DECEMBER 2023 FEG 221-ENGINEERING MATHEMATICS II LEVEL: 200 UNITS: 3 TIME: 2.5 HOURS Instruction: Answer Any Five (5) questions only. All questions carry equal marks. QUESTION-ONE (14 marks) a. For two forces a=(-31+2) N and 5 = (3i+6) N acting on a body, estimate the angle between (the direction of) the forces b. Find the root(s) of x²-2x+5=0 (10 marks) (4 marks) QUESTION TWO (14 marks) a. Using Linear Lagrange interpolation, estimate the value of lo, 12. given that log10-1.000 and log20 1.301 (10 marks) (4 marks) b. What is the error in the estimation? QUESTION THREE (14 marks) Find the root of f(x) = x²-13x + 7, using 'fixed point iteration. Choose (start from) x = 2.000, and stop at the fifth iteration xs (to 2 decimal places). Use the first term (x2) of the equation (f(x)), as your starting point, NOT the second term (x)! QUESTION FOUR (14 marks) 2. Show the first six terms of the serius: (1x)" (4 marks) b. Using the first six terms of the series (1-x)". estimate the value of (-3)5 21+1 c. Simplify (5 marks) (5 marks) 3+15 QUESTION FIVE (14 marks) Find the root of f(x)=x³-8, 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 Gaus: climination method to solve the following: x1+5x2+x3=12 2x-3x2+x=6 5x,+2x2-2x=2 (1) (2) (3)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
Problem 8P
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Transcribed Image Text:UNIVERSITY OF ABUJA
FACULTY OF ENGINEERING
ري
PROGRAMME: B.ENG
SECOND SEMESTER EXAMINATION 2022/23 SESSION - (12 DECEMBER 2023
FEG 221-ENGINEERING MATHEMATICS II
LEVEL: 200
UNITS: 3
TIME: 2.5 HOURS
Instruction: Answer Any Five (5) questions only. All questions carry equal marks.
QUESTION-ONE (14 marks)
a. For two forces a=(-31+2) N and 5 = (3i+6) N acting on a body, estimate the angle
between (the direction of) the forces
b. Find the root(s) of x²-2x+5=0
(10 marks)
(4 marks)
QUESTION TWO (14 marks)
a. Using Linear Lagrange interpolation, estimate the value of lo, 12. given that log10-1.000 and
log20 1.301
(10 marks)
(4 marks)
b. What is the error in the estimation?
QUESTION THREE (14 marks)
Find the root of f(x) = x²-13x + 7, using 'fixed point iteration.
Choose (start from) x = 2.000, and stop at the fifth iteration xs (to 2 decimal places). Use the first
term (x2) of the equation (f(x)), as your starting point, NOT the second term (x)!
QUESTION FOUR (14 marks)
2. Show the first six terms of the serius: (1x)"
(4 marks)
b. Using the first six terms of the series (1-x)". estimate the value of (-3)5
21+1
c. Simplify
(5 marks)
(5 marks)
3+15
QUESTION FIVE (14 marks)
Find the root of f(x)=x³-8, 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 Gaus: climination method to solve the following:
x1+5x2+x3=12
2x-3x2+x=6
5x,+2x2-2x=2
(1)
(2)
(3)
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