there are the question can you do it all so i can check my answers and workin out as well thanks

MASlGil: Fundamentals of li-"lathematies Semester 1? 2023 Assignment 5 - Due 5pm, IvIt:nnda3,.r 29 May 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. [15 marks] A ball is thrown straight up with an initial velocity of 4D mfs, so that its height [in meters) after t seconds is: Mt} = 2:90 a). (a) Find an expression for the velocity of the hall at time t. (b) "That is the instantaneous velocity at t = 4'? Is the hall rising or falling at this time? (c) "That is the maximum height achieved by the hall? Hint: the velocity of the ball will be zero when the hall is at its highest point. (d) How fast will the hall be travelling when it hits the ground? Hint: rst calculate time I? when the hall hits the ground. 2. [15' marks] Evaluate the following integrals (a) [23:4 3:1": +1d:r 2 . (b) [ ds: .1? (c) [195"! (2: Vi?) at: (d) fez no + 3} dz. 3. [8 marks] Find the equation of the tangent to the curve 1 = [3: mum? + 9 at. :1: = 4. 4. [8 marks] [3) Find d 1 dr (23:2 + 1}" (b) Hence evaluate [1 121" d , 1'". II (23:2 + 1}4 a Note: There are penalties for late aesignments. You must contact your tutor before the due date if you have difculties making the deadline