MA5164: Fundamentals of Mathematics Semester 2, 2022 ASSIGNMENT 3 Due by 11:59 pm, Friday '7 October Total Marks: 55 This assignment is worth 55 marks, with 5 marks reserved for presentation. Please note that marks will be deducted for solutions that are not properly presented, for working that is inadequate, or for untidy work. Always show full working. Where possible give the exact answer. 1. [4 marks] Evaluate the following (a) |47| |13| [2marks] (b) \"2 4| I5 +6|| [2 marks] 2. [14 marks] Let x) and g(x) be defined by ftx) =4x ax) = {:'; :2: (a) Evaluate gm), 345), max2). (f g)(4), (mm and (flax2} [markS] (b) Find all x for which f (x) = g{x). You must give the exact answer and show all working. [8 marks] 3. [8 marks] An open topped box is to be made by cutting out identical squares from the corners of a rectangular piece of cardboard then folding up the resulting flaps. Thus, if the side of each removed square has length x then the box height will also be x. If the cardboard has dimensions 70cm by 50cm find an expression for the volume of the box V (x) in terms of x. What is the domain of this function? What sort of function is it (quadratic, cubic, rational or. . .)? 4. [24 marks] Evaluate the following limits (using calculus and showing all your working) (a) limxmo $23] [4 marks] (bl limxwo % [4 marks] (c) limx_,_m % [4 marks] {d} 1iTrix>2 fazfgifz [4 marks] (e) limxl3 x2334 [4 marks] (3 limxld- {if [4 marks] c There are penalties for late assignments. You must contact your tutor before the due date if you have difficulties making the deadline. 'k'k'k'k'k'k'k