常用二重极限

$$\underset{(x,y)\to (0,0)}{\lim }\frac{xy}{x^2+y^2}不存在$$ $$\underset{(x,y)\to (0,0)}{\lim }(x+y)\ln (x^2+y^2)=0$$ $$\underset{\rho \to 0}{\lim }\frac{e^{-1/{\rho }^2}}{\rho }=\underset{\rho \to 0}{\lim }\frac{\frac{1}{\rho }}{e^{1/{\rho }^2}}=\underset{x\to \infty }{\lim }\frac{x}{e^{x^2}}=0$$