Question 11.5.4: Where are the functions given by the following formulas cont......

Essential Mathematics for Economic Analysis [1185377]

Where are the functions given by the following formulas continuous?

(a)\,f(x,y,z)=x^{2}y+8x^{2}y^{5}z-x y+8z

\quad\quad({\bf b})\;g(x,y)=\frac{x y-3}{x^{2}+y^{2}-4}

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(a) As the sum of products of positive powers, f is defined and continuous for all x, y, and z.
(b) The function g is defined and continuous for all pairs (x, y) except those that lie on the circle x² + y² = 4. There the denominator is zero, and so g(x, y) is not defined.

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