(a) Suppose f(x, y) = f(r cos 0,r sin 0) = g(r, 0) and assume that...

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(a) Suppose f(x, y) = f(r cos 0,r sin 0) = g(r, 0) and assume that all their partial derivatives are continuous. Show that (i) (ii) (V.V)² f = V.Vf= V.Vf= v=10 (13²) + 71 200 ag rər Ər (iii) Find the terms A(r), B(r), C(r) and D(r) such that 0¹g 20³g 1 8²g 1 ag Ər4 r² Ər² ³ Ər +A(r); + B(r) + a²fa²f + əx² dy² - r Ər³ Jªg Ər²20² + 8³g Ərə0² g 204 + C(r). + D(r) (3 marks) (6 marks) 8²g 20² (6 marks) (a) Suppose f(x, y) = f(r cos 0,r sin 0) = g(r, 0) and assume that all their partial derivatives are continuous. Show that (i) (ii) (V.V)² f = V.Vf= V.Vf= v=10 (13²) + 71 200 ag rər Ər (iii) Find the terms A(r), B(r), C(r) and D(r) such that 0¹g 20³g 1 8²g 1 ag Ər4 r² Ər² ³ Ər +A(r); + B(r) + a²fa²f + əx² dy² - r Ər³ Jªg Ər²20² + 8³g Ərə0² g 204 + C(r). + D(r) (3 marks) (6 marks) 8²g 20² (6 marks)