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What is the purpose of the capacitors between 5V and ground on the power pins of the op-amps?enter image description here

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It looks like these are just some decoupling capacitors. Their purpose is to clean out any noise from the power line (on the pcb caused by other parts) and from the device itself. Technically the op-amps would work without them (only do this for testing purpose) but it is always good practice to put them on any integrated circuit you have in your design. Some times the ic manufacturer will give you instructions about the capacity, but 100nF (0.1uF) is a very common value and my goto value if nothing is specified. These capacitor will not dramatically increase your BOM you can get them for around 0.1USD (single pice) or even cheaper when buying a higher amount. But they will increase the reliability of your design. You can find some more information here: https://en.m.wikipedia.org/wiki/Decoupling_capacitor

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