(i) Use the linear appraximation formula

  • June 25, 2021

(i) Use the linear appraximation formula△y≈f(x)△x orf(x+△x)≈f(x)+f(x)△x with a suitable choice of f() to show thatlog(1+50)≈50 for small values of1/10 (ii)Use the result obtained in part ( a)above to approcimate log(1+50) de.1/10 (ii)Check your result in (b)by evaluating log(+50) de exactly using in- tegration by parts ()An electromotive force (emf) of 100 sin 2t volts is applied to a circuit comprising a resistance of 5 ohms in series with an inductance of 20 henries. The current i(t) in the circuit at time t is given by20+5i=100sin2t. Initially (at t =0) the circuit is dead (i.e. i =0). (i) Solve the given linear differential equation to find i(t).(i) Hence, determine the’steady-‘cun-sate,ie. the current after consider- able time

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