Let f(x,y) = ( 3*(x^2)*y ) / ( (x^2) + (y^2) )
Where is f continuous?
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We've been taught that a polynomial in x, y is continuous everywhere on R^2
How do we find the continuity of a function like this when there are 2 different functions kind-of-terms in both numerator and the denominator?
f(x,y) is a rational function of x and y, so it is continuous everywhere in R^2 except where the denominator is zero.
clearly, x^2+y^2 = 0 only at (0,0)