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Last week I had an exam in advanced calculus. One of the questions asked about the continuity of a function of three variables.

However, the doctor gave me 0 out of 3 for the question while i am sure that my answer is correct and i told him that but he insisted that its wrong.

can you help me?

Question:

Discuss the continuity of the function f(x,y,z)=8xy/(x^2+y^2-z)

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Doctor's Answer:

the function is continuous in all the points except the points lying on the

circular paraboloid z=x^2 + y^2

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My answer:

the domain of f(x,y,z) is all the point lying inside or outside (but not on) the

circular paraboloid z=x^2 + y^2

the function is continuous in all the points that lie inside or outside the

circular paraboloid z=x^2 + y^2

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Thank you very much