Consider again the differential equation modeling the current in a closed circuit consisting of a battery (supplying the external emf Es(t)), a resistor, and an inductor: (1) Ee(t) = RI + Lal, 1(0) =0 dt ' Let's assume that battery is switched off according to the discontinuous (step) function, Ee(t ) = Eo , if 0 T . Here, Eo > 0 is the constant initial voltage supplied by the battery and T > 0 is the time at which the battery is switched off. (c) Use the strategy from the WS "Linear first order equations - Discon- tinuous source terms," part (b) to solve (1). (d) We constructed the solution I(t) of (1) so that it is continuous for all t, and in particular at t = T. Is the solution that you obtained in part (c) also differentiable at t = T? The answer to this question requires a computation, see the hint below Hint: Recall from single variable calculus, that since I(t) is a piece- wise function, in order to analyze differentiability you need to go back to the definition: 2) I(t) is differentiable at t = 7 - lim I(t) - I(T) lim I(t) - I(7) exist . t - T t - T Hence, in order to answer the question about differentiability, you need to compute the left and right limit of the difference quotient as MATH 234 - DIFFERENTIAL EQUATIONS indicated in (2) and see whether the two agree or not. De l'Hospital will be useful