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my book states that it is comparing how much a function y(t) is like a standard function. what exactly does the answer mean such as y(s)=1/(s-2)

is this the differnence between the functions depending on the value of s

and further more how does taking the integral from zero to infinity of two functions tell me how much alike they are

stupid vague books i hate when they pull equations out of the air and don't explain where they come from and what they mean