exo7 1794

$$f(x,y) = \left\{ \begin{array}{cc} \frac{x^2y^2}{x^2+y^2} & \mbox{ si }(x,y) \neq (0,0) \\ 0 & \mbox{ sinon. } \end{array} \right .$$

$$f(x,y) = \left\{ \begin{array}{cc} \frac{x^2y}{x^2+y^2} & \mbox{ si }(x,y) \neq (0,0) \\ 0 & \mbox{ sinon. } \end{array} \right .$$

$$f(x,y) = \left\{ \begin{array}{cc} \frac{x^4y}{x^4+y^6} & \mbox{ si }(x,y) \neq (0,0) \\ 0 & \mbox{ sinon. } \end{array} \right .$$

$$f(x,y) = \left\{ \begin{array}{cc} \frac{xy^4}{x^4+y^6} & \mbox{ si }(x,y) \neq (0,0) \\ 0 & \mbox{ sinon. } \end{array} \right .$$

$$f(x,y) = \left\{ \begin{array}{cc} y^2\sin \frac{x}{y} & \mbox{ si }y \neq 0 \\ 0 & \mbox{ sinon. } \end{array} \right .$$

$$f(x,y) = \left\{ \begin{array}{cc} xe^{\arctan \frac{y}{x}} & \mbox{ si }x \neq 0 \\ 0 & \mbox{ sinon. } \end{array} \right .$$