2.7.60 Function properties

Condition: Investigate the function \( f \) for continuity and differentiability at the point \( (0; 0) \). \[ f(x, y)=\left\{\begin{array}{c} \tan \frac{x}{\sqrt{x^{2}+y^{2}}}, \quad x^{2}+y^{2} \neq 0 \\ 0, \quad x^{2}+y^{2}=0 \end{array}\right. \]