\[f(x,y)=\left\{ \begin{array}{cc} \frac{(x+2y)^3y^3}{x^4+y^4} & \mbox{ si }(x,y) \neq (0,0) \\ 0 & \mbox{ sinon. } \end{array} \right .\]
\[f(x,y)=\left\{ \begin{array}{cc} \frac{x^6+x^2y^2}{x^2+y^2} & \mbox{ si }(x,y)\neq (0,0) \\ 0 & \mbox{ si }(x,y)=(0,0) \end{array} \right .\]
\[f(x,y)=\left\{ \begin{array}{cc} e^{\frac{x}{y}} & \mbox{ si }y \neq 0 \\ 0 & \mbox{ sinon. } \end{array} \right .\]
\[f(x,y)=\left\{ \begin{array}{cc} \frac{\sin xy}{y} & \mbox{ si }y \neq 0 \\ x & \mbox{ sinon. } \end{array} \right .\]
\[f(x,y)=\left\{ \begin{array}{cc} \frac{\ln (1+x)-\ln (1+y)}{x-y} & \mbox{ si }x \neq y \\ \frac{1}{1+x} & \mbox{ sinon. } \end{array} \right .\] définie sur \(D=\{(x,y) \mid x\geq 0, y\geq 0\}\).