(8) Show that the function f(x, t) = et cos () satisfies heat equation ft = c' fix. (9) Determine whether there exists a function f(x, y) such that f.(x, y) = x + 4y and fy(x, y) = 2x - y. Explain your reasoning. (10) In a chemical reaction, the temperature ?', entropy S, Gibbs free energy G and enthalpy H are related by G = H - TS. H (a) Show that a(G/T) = aT (b) Show that a(G/T) H. Chemists measure the enthalpy of a reaction by measuring a(1/T) this rate of change. (11) Find the total differential if = = ysinx - cosy