TW39 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING B.ENG (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATION SEMESTER 1 - 2015/2016 INTRODUCTORY ENGINEERING MATHEMATICS MODULE NO: EEE4001 Date: Tuesday 12 January 2016 Time: 2:00 - 4:00 PAST EX ABBATE NATIOADQ1 KATHEM INSTRUCTIONS TO CANDIDATES: There are SIX questions. Answer ANY FOUR questions. All questions carry equal marks. Marks for parts of questions are shown in brackets. Electronic calculators may be used provided that data and program storage memory is cleared prior to the examination. CANDIDATES REQUIRE: Formula Sheet (attached). --
Page 2 of 10 School of Engineering BEng (Hons) Electrical and Electronic Engineering Semester 1 - 2015/16 Introductory Engineering Mathematic Module No: EEE4001 Q1 The following five electrical circuit quantities are given by: Z1=5cis45°, Z2 =- 3i , I=1+i, I2=3<30° , V =2e3 Ti Where i2 = - 1, Z is the impedance, I is the current and V is the voltage (a) Calculate the total current I1 + I2 and express the answer in polar form [4 marks] (b) Express Z1+ Z2 ZZ2 in exponential form: [7 marks] (c) Express V in Cartesian form: V = x+iy [2 marks] (d) Find the real and imaginary parts of (1 + ¡4 )3 [4 marks] (e) Find the (I - I2 } and express the answer in rectangular form [8 marks] Total 25 marks Please turn the page
Page 3 of 10 School of Engineering BEng (Hons) Electrical and Electronic Engineering Semester 1 - 2015/16 Introductory Engineering Mathematic Module No: EEE4001 Q2 (a) Expand and Simplify the expression: ln 2x XVx+1 e [3 marks] (b) Find the solution for ex++x-6 - e2x = 0 GePER (c) A small business sells £20,000 worth of sports memorabilia during its first year. The owner of the business has set a goal of increasing annual sales by £8000 each year for 24 years. Assuming that the goal is met, find the total sales during the first 25 years this business is in operation. que VAN Cia [4 marks] (d) By using binomial series to evaluate V1.05 and correct to 5 decimal places: [6 marks] e x >00 x (e) Use L'Hôpital's rule to find limiting values for lim -x PAST EXER PAINT [9 marks] Total 25 marks Please turn the page