By considering different paths of approach, show that the function has no limit as $(x,y)\to(0,0)$.\\
$f(x,y) = \frac{x}{\sqrt{x^2 + y^2}}$\\Find the limit as $(x,y)\to(0,0)$ along the path $y = x$ for $x > 0$.\
(Type an exact answer, using radicals as needed.)\\Find the limit as $(x,y)\to(0,0)$ along the path $y = x$ for $x < 0$.\
(Type an exact answer, using radicals as needed.)\\Why doesn't the limit exist?\\
A. The limit does not exist because $f(x,y)$ is not defined at the point $(0,0)$.\nB. The limit does not exist because $f(x,y)$ has the same limits along two different paths in the domain of $f$ as $(x,y)$ approaches $(0,0)$.\nC. The limit does not exist because $f(x,y)$ is not continuous.\nD. The limit does not exist because $f(x,y)$ has different limits along two different paths in the domain of $f$ as $(x,y)$ approaches $(0,0)$.
