ࡱ> Y[X'` bjbj uO" " " 4V EEEhFFV 7GIR@J@J@JKKK$Ohܿ" N}K"KNNܿ@J@J=SSSN@J" @JSNSS~?t " @JG -S<E~OXz<07Z?P? ?" pKiLSLtmM_KKKܿܿR^KKK7NNNNV V V $/V V V /V V V   LEARNER NAME ASSESSOR NAME  F. NDORO DATE ISSUED HAND IN DATE SUBMITTED ON   CriteriaTaskAchievedFeedback P10 apply the basic rules of calculus arithmetic to solve three different types of function by differentiation and two different types of function by integration.  Task 1  D1 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using calculus  Task 2  D2 apply the rules for definite integration to two engineering problems that involve summation.  Task 3  This brief has been verified as fit for purpose  Internal Verifier ANTHONY SPICER Signature A J Spicer Date 27/07/2012 Assessor's commentsQualificationEdexcel Lev 3 National Diploma in EngineeringAssessor nameF. NDOROUnit number and titleUnit 4 Mathematics for Engineering Technicians (A/600/0253)Learner nameAssignment title ASSIGNMENT FOUR CALCULUS TECHNIQUESGrading criteriaAchieved? P10 apply the basic rules of calculus arithmetic to solve three different types of function by differentiation and two different types of function by integration.  D1 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using calculus D2 apply the rules for definite integration to two engineering problems that involve summation. Learner feedbackAssessor feedbackAction planAssessor signatureDateLearner signatureDate TASK 1 Basic rules of integration and differentiation P10 apply the basic rules of calculus arithmetic to solve three different types of function by differentiation and two different types of function by integration. 1. Find the derived function of the following functions: (a) y = 8 EMBED Equation.3  (b) y =  EMBED Equation.3  (c) y = 6 EMBED Equation.3  -20 EMBED Equation.3  + 5 (d)  EMBED Equation.3  (e)  EMBED Equation.3  : [P10 PART] 2. Express  EMBED Equation.3 as a function of EMBED Equation.3 , if: (a)  EMBED Equation.3  = 3 EMBED Equation.3  + 4 EMBED Equation.3  (b)  EMBED Equation.3  = 4 EMBED Equation.3  - 3 EMBED Equation.3  + 6 (c)  EMBED Equation.3  (d)  EMBED Equation.3  (e)  EMBED Equation.3  : [P10 PART] TASK 2 APPLICATIONS OF CALCULUS IN ENGINEERING SOLUTIONS (DIFFERENTIATION) D1 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using calculus 1. For a certain material, Newtons law of cooling can be represented by the decay equation EMBED Equation.3 where t is the time in seconds. And EMBED Equation.3 is the temperature at any given instant in time. (a) Plot EMBED Equation.3 against t at 0.5sec intervals for EMBED Equation.3 (b) From your graph, find the initial temperature and the temperature that the body approaches as time increases to infinity. (c) Determine the slope at t = 3 seconds both from the graph and by differentiation and give your comment as you compare the results. : [D1 part] 2. The voltage across a capacitor C when it is being discharged through a resistor R is related to time t by the equation EMBED Equation.3where T is the time constant and T = CR. (a) Plot a graph of voltage EMBED Equation.3 against time EMBED Equation.3 (b) From your graph, find the voltage and rate of change of voltage after 0.2 seconds given that R= 12kEMBED Equation.3and C = 22EMBED Equation.3 (c) Check that your answers in (b) are correct by differentiation : [D1 part] TASK 3 APPLICATIONS OF CALCULUS IN ENGINEERING SOLUTIONS (INTEGRATION) D2 apply the rules for definite integration to two engineering problems that involve summation. 1. The total charge passed on to a battery is represented by the area under a graph of current against time. The law of the graph is EMBED Equation.3. Determine the charge after 7 seconds. : [D2 part] 2. The velocity of a falling object is related to time by the law EMBED Equation.3. The distance fallen is the area under the velocity time graph. Calculate the distance fallen 10 seconds after release. : [D2 part] Student declaration I declare that all the work submitted for this assignment is my own work or, in the case of group work, the work of myself and the other members of the group in which I worked, and that no part of it has been copied from any source. 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