Consider two functions f and g, where f(x, y) = g(r, 0) and x = r cos 0, y = r sin 0. (a) With the use of a diagram, identify all the relationships between f, g, x, y,

 

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Consider two functions f and g, where f(x, y) = g(r, 0) and x = r cos 0, y = r sin 0. (a) With the use of a diagram, identify all the relationships between f, g, x, y, r and 0. (b) Treat a = r cos, y = variables, determine r sin as implicit functions with x and y being 00 00 Ər Ər and dax' dy' dx' ду (c) From the given information, we know that f = 9, therefore we can say fr 9. Using this reasoning, express fa, fu, fer and fuy in terms of r, 0 and partial derivatives of g. [Hint: in part (a), f can be replaced by fa without affecting the relationship.] 1 (d) Hence, or otherwise, show that fax + fyy=9rr +=9r+ T' 1 r2.900.

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