EEC 209 Mathematics 1 Exam 2026

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EEC 209: End-of-semester examination for EEC209, Mathematics I, Department of Electrical Engineering, University of Buea, First Semester 2025/2026 (4 February 2026). Exercise 1 (21 marks) is a set-theory and logic problem: given that in a town 25% of families own a phone, 20% own a car, 60% own neither, and 2000 families own both, the student must determine the total number of families, then the counts owning a car and a phone, neither, car only, and phone only; a second part asks for the converse, negation, and contrapositive of the statement 'If a sequence {x_n} increases and is bounded then {x_n} is convergent.' Exercise 2 (49 marks) covers calculus and analysis: finding the third-order Taylor polynomial of g(x)=sin(x) about x0=0 and deducing the limit of sin(x)/x as x tends to 0; using the Intermediate Value and Rolle theorems to show f(x)=x^3+x-1 has a unique root a0 in (0,1); approximating a0 via Newton-Raphson iteration (computing x2 through x6 to six decimal places and the value to four decimal places); and determining the nature, characteristics, and sketch of the set of points in the plane satisfying the conic equation 9x^2+4y^2-18x-8y-23=0 (an ellipse in general position), worth 17 of the exercise's marks.