14 marks 6. (a) (6 marks) Suppose that a function f(x, y) has the following form in polar coordi- nates: f (r cos 0, r sin 0) = rtand if 0 2 { 3, 3x ] 0 if 0 6 { x, 3m . Is it true that lim(z,3)->(0,0) f(x, y) = 0? Prove your answer. (In this part, an e - 6 proof is not required.) Solution: It is not true. To see this, consider the trajectory where rtand = 1, 0 oo as 0 -> x/2, we haver -> 0 but f(r cos0, r sine) = 1 along that trajectory