1.(25 points) Vapor-liquid equilibria (y-x values) in a binary system is commonly described by the equation: y[x(t)] = ax(1) 1+(a-1)x(t) where: a = relative volatility; assume this is a known constant x(t)-time-dependent mole fraction of a component in the liquid phase; assume x(0)=x, is a known constant y(t) = time-dependent mole fraction of a component in the vapor phase; assume y(0)=y, is a known constant Derive the Taylors series approximation for y[x(t)] ?? and write your answer in the box below. Any differentiation must be done manually, i.e. without using any electronic device including a calculator. You must show all steps in deriving your solution. y[x(t)]=