i. For the circuit of Figure 1.1: V; (1) ww 50ΚΩ M V(1) + 1 μF v (1) 200 Κ Ω 1 μF Figure 1.1 a. Derive the transfer func

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i. For the circuit of Figure 1.1: V; (1) ww 50ΚΩ M V(1) + 1 μF v (1) 200 Κ Ω 1 μF Figure 1.1 a. Derive the transfer function relating the input voltage v, and output voltage v.. b. Determine function vo(t) when a 4V step input is applied. c. Using the initial and final value theorem, find the initial and final value of the output voltage when the input in part b above is applied? ii. For the following function, determine if pole-zero cancellation can be approximated. F(s) (s + 3) (s +2.5) (s+4)² iii. Consider the following differential equation: dx d²x +5. + 8x = f(x) dt² dt where f(x) is the input and a function of the output x. If f(x) = e-x, linearize the differential equation for x near 0.