Q$1)(10$ pts$)($a$)$ certain operational amplifier has a Common$-$Mode Rejection Ratio $=250,000$ and an Open$-$Loop Gain$=80,000,$ calculate the common$-$mode gain

$($b$)$ if the slew rate $=0\mathrm{.}5\frac{V}{}s,$ what is the maximum frequency at which the amplifier can output an undistorted sinusoidal signal with an amplitude of $10$ Vpp $?$

$($c$)$ use this opamp to design a none inverting amplifier that has a closed loop voltage gain of $5,$ what is the closed loop bandwidth given that the open loop cutoff frequency $=10Hz.$

$($d$)$ calculate the unity$-$gain bandwidth for this amplifier and discuss the trade$-$off between gain and bandwidth in operational amplifiers.