Scenario: You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. They have asked you to undertake a series of such evaluations. Activity Task 1: Differentiate each of the following current functions with respect to time and hence determine the 'rate of change' for each of the functions when time, t, is 3 seconds. al i= (3c+5)4 b) i= (4:3 2r + 3)3| c] r' = log.(3tz) d) i = 299:") e) i= sin(5t3 + 6: 3) n r = 42"" ('1 Task 2: PART 1 For the circuit shown below, assuming zero charge on the capacitor att = 0, the current owing may be quantied as: _; ' _ E r=e R Integrate this equation with respect to t and hence nd the charge stored in the capacitor 0.5 seconds after the switch is closed. n 1n11 turn..." I "I All Baal-Ir anus..." Irltm , 'Irn'n'sn'n on": x n' c PART 2 The current (iz) through a 100 mH inductor (L) has a relationship with time (t) as follows: in = =1 cos(300t) dt Determine the inductor current when the time is 0.75 seconds. Task 3: PART 1 Determine the area under the following exponential growth curve between 1 seconds and 5 seconds: y = [ ( 1 - e - 2 ) at PART 2 Determine the area under the following exponential decay curve between 3 seconds and 7 seconds: y = [(e-21) at Task 4: PART 1 Locate the co-ordinates of the turning point for the following function and determine whether it is a maxima or minima: y = 7x2 - 3x PART 2 Find the maxima and minima values for the function: y= x3 - 3x + 2