- June 25, 2021
. (a)() Use the linear appronximation fornula△y≈f(x)△x orf(x+△x)≈f(x)+f(x)△x with a suitable choice of (() to show thatog(1+50)≈50 for smnall values of 01/10 (i) Use the result obtained in part (a) above to approximate log(1+50)1/0 (iii) Chedk your result in (b) by evaluatinglog(1+50 d0 exactly uing in tegration by parts. (b) An electromnotive force (emf) of 100 sin 2t volts is applied to a circuit comprising a resistance of 5 ohmns in series with an inductance of 20 henries. The current i() in the cireuit at time is given by20+5i=100sin2t Initially(att=0) the circuit is dead(ie.i=0) ( Solve the given linear differential equation to find i(). () Hence, deternine the ‘steady-state’ current, ie. the current after a condder. abke time.