Déterminer les limites lorsqu’elles existent:
1
\(\lim_{(x,y)\to (0,0)} \frac{x}{x^2+y^2}\)
2
\(\lim_{(x,y)\to (0,0)} \frac{(x+2y)^3}{x^2+y^2}\)
3
\(\lim_{(x,y)\to (1,0)} \frac{\log (x+e^y)}{\sqrt{x^2+y^2}}\)
4
\(\lim_{(x,y)\to (0,0)} \frac{x^4+y^3-xy}{x^4+y^2}\)
5
\(\lim_{(x,y)\to (0,0)} \frac{x^3y}{x^4+y^4}\) ;
6
\(\lim_{(x,y)\to (0,0)} \frac{(x^2+y^2)^2}{x^2-y^2}\) ;
7
\(\lim_{(x,y)\to (0,0)} \frac{1-\cos xy}{y^2}\) ;
8
\(\lim_{(x,y)\to (0,0)} \frac{\sin x}{\cos y-\cosh x}\)