The calculated resistors values are R1=2.7kΩ, R2=18kΩ, R3=10kΩ, R4=1kΩ, R5=51Ω and the capacitance values are as shown in the figure. Are the capacitance values given fixed for every case or there are any theoretical method and calculations involved to got those capacitance values to design a band-pass filter response with cutoff frequencies of approximately 16Hz and 16kHz? If yes, what are the calculations involved? And what is the purpose of using R8 in this audio amplifier?

 

You know F=1/(2x3.14xRxC)
C3 blocks the low frequency and DC. The input impedance is a low 1K. I think that works out to 16hz.
High frequency role off is by C6 and the impedance for that is 20k. 17khz.