Question

Show that g(x,y)= (x^2-y^2)/(x^2+1) is a continuous function. I know from regular calc that if I have a composite function where both functions are continuous, then it is continuous. I know that both are continuous by looking at the graph, but how do I prove so otherwise?

Answer 1

evalúa la función con esto \[\lim_{x,y \rightarrow a,b}g(x,y)=g(a,b)\]
pero principalmente recuerda que g(x,y) al se racional es el cociente de dos polinomios y todos los polinomios en R^2 son continuos por tanto "una función racional es continua en todo su dominio".