Suppose that ;

1) such that :

2)The Euclidian norm of a vector is defined as :

3) The maxnorm of a vector is defined as :

Where belong to the real Nos R

Then prove :

,with respect to both norms

I know that i have to prove the following:

1) given ε>0 ,i got to find a δ>0 ,such that :

if 0<|x|<δ , then

2)given ε>0 ,i must find a δ>0 ,such that:

if 0<|x|<δ ,then .

Any suggestions for that delta??