Given the function $f(x, y) = \arctan(\frac{y}{x})$ defined for $(x,y)$ with $x>0$, how can we find Taylor polynomial in point $x_0=0$? As I understood, Taylor polynomials for $n=1$ for functions with two variables are the same as tangent plane, right?
In addition, how can we prove that $f$ doesn't have a limit value in point $x_0 (0, 0)$?