In Exercises 1–3, begin by drawing a diagram that shows the relations among the variables. 1. If w = x? + y² + z² and z = x² + y?, find Əw a. aw b. dz дw c. ду, дz х 2. If w = x2 + y – z + sin t and x + y = t, find %3D *). aw дw b. dy, a. c. ду z, 1 дz х, у х, Z (). Əw дw f. дt у, г d. e. az y, t at x, z 3. Let U = f(P, V, T) be the internal energy of a gas that obeys the ideal gas law PV = nRT (n and R constant). Find (). (); a. b. ӘР

6.1.4 Let A = [1,3], B = [2,4] and C = [2,3]. Prove or disprove that (Ах В)n (В х А) — СхС. C x Hint: Draw the sets A x B, B × A and C x C in the Cartesian plane. The picture will give you a hint on whether or not the statement is true, but it does not constitute a proof.