1. The problem statement, all variables and given/known data Show that the function f(x,y)= xy/sqrt(x^2+y^2) is continuous at the origin using polar coordinates. f(x,y)=0 if (x,y)=(0,0) 2. Relevant equations r=sqrt(x^2+y^2) x=rcos(theta) y=rsin(theta) 3. The attempt at a solution So, converting this equation to polar coordinates, I get rsin(theta)cos(theta). However, after this I'm stumped as to how I prove that this is continuous at the origin.