For each part of this problem, a system is described that generates an output waveform y(t) from an input waveform x(t). For each part, state whether the system described is: (i) linear or non-linear, (ii) time-invariant or not-time-invariant, (iii) memoryless or "with memory." (Three answers are required for each part: (a-i), (a-ii), (a-iii), etc.) Explain your reasoning. (a) y(t) = 4 dx(t)/dt (b) y(t) = 6 integral^t_0 x(tau) d tau (c) y(t) = 2 x^3 (t) (d) y(t) = cos(2 pi t) x(t) (e) y(t) =5 |x(t)| (f) y(t) + 4 dy(t)/dt = 3 x(t - 3) (g) y(t) is a voltage across a capacitor in an electrical network formed by connecting standard resistors, inductors, and capacitors, and the input x(t) is the current supplied by a current source connected to the circuit ... for example, between a reference ground and a node in the circuit