A limit

[triclino]

Suppose that ;

 

1)[math] f: R\rightarrow R^2[/math] such that : [math]f(x) =(2x+1,x^2)[/math]

 

2)The Euclidian norm of a vector [math] v=(u_{1}, u_{2})[/math] is defined as :

 

[math] ||v||_{Eu} =\sqrt{ u_{1}^2 +u_{2}^2}[/math]

 

3) The maxnorm of a vector [math] v=(u_{1},u_{2})[/math] is defined as :

 

[math] ||v||_{max} = max( |u_{1}|,|u_{2}|)[/math]

 

Where [math] u_{1},u_{2}[/math] belong to the real Nos R

 

Then prove :

 

[math] \lim_{x\to 0} f(x) = (1,0)[/math] ,with respect to both norms

Edited January 21, 2010 by Cap'n Refsmmat
fixed that \lim for you