exo7 1787

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

\(\lim_{(x,y)\to (0,0)} \frac{\sin x}{\cos y-\cosh x}\)