exo7 1809

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

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

$$f(x,y)=\left\{ \begin{array}{cc} e^{x \ln (x^2+y^2)} & \mbox{ si }(x,y) \neq (0,0) \\ 1 & \mbox{ sinon. } \end{array} \right .$$