Please if you can solve this problem :S
http://www13.0zz0.com/2009/11/19/17/395971290.jpg << Continuous not Constant
Please if you can solve this problem :S
http://www13.0zz0.com/2009/11/19/17/395971290.jpg << Continuous not Constant
Just notice by the triangle inequality $\displaystyle \vert x\frac{x^2-y^2}{x^2+y^2} \vert \leq \vert x\frac{x^2+y^2}{x^2+y^2} \vert = \vert x \vert$ so take $\displaystyle \vert x \vert \leq \Vert (x,y) \Vert \leq \delta = \epsilon$ and plug it in the definition of continuty. This gives you that the function is continous at 0, for every other point it's clearly continous since it's the quotient of cont. functions and the denominator does not vanish in any other point.