Consider two functions f and g, where f (x, y) = g(r, 0) and x =...

 

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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 rsinas 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 f = 9. Using this reasoning, express fa, fu, fre 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 + fuy = 9rr + =9r+ T' 1 r2.900. 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 rsinas 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 f = 9. Using this reasoning, express fa, fu, fre 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 + fuy = 9rr + =9r+ T' 1 r2.900.

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a Diagram illustrating the relationships between f g x y r and f y r x In the diagram we have f The function f depends on x and y g The function g dep... View the full answer