(a) Derive the expression for the closed-loop voltage gain \(A_{v}=v_{O} / v_{I}\) for the circuit shown in Figure P9.46. Assume an ideal op-amp.

(b) Let \(R_{4}=50 \mathrm{k} \Omega\) and \(R_{3}=25 \mathrm{k} \Omega\). Determine \(R_{1}\) and \(R_{2}\) such that \(A_{v}=6\), assuming the maximum resistor value is limited to \(200 \mathrm{k} \Omega\).

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