Hong Kong Community CollegeSEHH1068 Foundation MathematicsAssignment 2Expected Learning Outcomes: use a variety of quantitative methods. identify and apply appropriate techniques for the solution of common mathematical problems. apply probabilistic techniques to analyse problems in real-life situations. apply the mathematical knowledge and reasoning skills needed in their future studiesPlease READ the following instructions before start working on this assignment.1. You have 120 minutes PLUS 15 minutes to complete and submit your assignment.2. Answer all questions in the answer book provided.3. All answers must be written in ink (red is not preferred).4. Total marks of this question paper are 100 marks.5. There are FOUR questions in this paper.6. Express your final answer to exact values whenever necessary.7. Show all your workings clearly and neatly. Reasonable steps should be shown.8. Show all the details when applying elementary row operations in a question.9. Make sure that you have submitted the correct and entire PDF file (with file size limited at 20MB) for thesubject concerned.10. The filename of your submission is ‘1068assign2’.Page 2 of 3IMPORTANT Answer ALL questions on the answer booklet provided. Each student is required tocomplete this assessment individually using his/her student ID number. The method is shown below.R = the 4th digit of your student ID plus ONEExample: If your student ID number is 21098765, then R = 9 + 1 = 10.Question 1 (20 marks)Use Gauss–Jordan elimination with Elementary Row Operations to solve1 2 3 12x23x34x1,8.1 2 36 4 7x x x (Hint: You are required to state the values of x1 2 3 , and x x .) 1,x x x RQuestion 2 (20 marks)Consider the following system of linear equations 3233 4txt t x1 22 3x x 1,2 ,tt m1 2x x 3x1,13x 24x Rwhere t and m are real constant. (a) Suppose1 12 31t0 0 1 2 21 3 3R R RR R R t23 4 3 4 2t t t m R0 _ _ _ 2 3 32 3R R R .Use Elementary Row Operations to determine , , and in terms of t and m.(b) Hence, find all the value(s) of t m and , if any, such that the given system of linear equations has(i) unique solution(ii) no solution(iii) infinitely many solutions.Page 3 of 3Question 3 (30 marks)(a) Find the largest possible domain of 1 2 3( )4x x x xf xx R.(b) Determine with reason(s) whether the following functions f ( ) and ( ) x g x is odd, even or neither.(i) f ( ) sin x x x 3 2(ii) g x x ( ) 7 3 R(iii) h x x ( ) 4(c) Find the periods of the function cos . 2x4f x Question 4 (30 marks)(a) Let x2f xxRfor x 2 .(i) Determine the inverse function of f ( ) x , i.e. f 1( ) x .(ii) Find the function g such that g f x x ln 2 .(b) Evaluate the following limits(i) 1 1limx 1 2x x x x R (ii)5lim5 x 2 1x x *** End of Paper ***

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