Task $3$ In this exercise, you will do filter design from sketch.

$1.$ Suppose that you want to build a low$-$pass filter which has the cut$-$off frequency of $100$ Hz $,$ fix the capacitor to $1$ uF and choose the correct resistor. Find the correct resistor and sketch the circuit on paper. Remark: Include the process of finding the correct resistor. And on your sketch, you must specify the resistance of your selected resistors.

$2.$ Suppose that you want to build a high$-$pass filter which has the cut$-$off frequency of $\backslash (\backslash$mathbf$\{500$ H z$\}\backslash ),$ fix the capacitor to $10$ uF and choose the correct resistor. Find the correct resistor and sketch the circuit on paper. Remark: Include the process of finding the correct resistor. And on your sketch, you must specify the resistance of your selected resistors.

$3.$ You have two capacitors $\backslash (\backslash$mathrm$\{$C$\}1=1\backslash$mathrm$\{$uF$\},\backslash$mathrm$\{$C$\}2=10\backslash$mathrm$\{$uF$\}\backslash ),$ choosing the correct resistors and build a bandpass filter of $\backslash ([100\backslash$mathrm$\{$~Hz$\},500\backslash$mathrm$\{$~Hz$\}]\backslash ).$ Sketch the circuit on paper. Remark: Include the process of finding the correct resistor. And on your sketch, you must specify the resistance of your selected resistors.

$4.$ Built your step $3$ solution in breadboard and verify the performance.