1. The problem statement, all variables and given/known data The real valued function f of two variables is defined by f(x,y) = tan( (1/2) *(pi) *sqrt( (x^2 + y^2) )/( sqrt( (x^2 + y^2) ) for each (x,y) satisfying 0 < x^2 + y^2 < 1. How should f(0,0) defined so that f is continuous at (0,0)? 2. Relevant equations 3. The attempt at a solution I wasn't sure whether the question was asking show the limit exists or doesn't exist? I think asking me to show it exists. I tried using polar co ordinates y=r*sin[tex]\theta[/tex] , x=r*cos[tex]\theta[/tex] =tan( (1/2) * (pi) * r) / r = 1/cos( (1/2) * (pi) * r ) * sin((1/2) * (pi) * r)/r = 1 * sin((1/2) * (pi) * r)/r I got stuck here was trying to use the identity lim->0 sinx/x = 1 I know you can use squeeze theorem to prove limits exist, but I don't really understand how it works for two variables. In one variable limits if 0 < |x-a|<[tex]\delta[/tex] then |f(x)-L|< [tex]\epsilon[/tex] but in two variable limits what is |x-a|?