4. Functions are defined via sequence limits. Find the domains of these functions (i.e. all values of x for which the limits do exist) and sketch the graphs of these functions.

n2 +2n+1n+1 I. lim 2 ,

n2 +2n+1n+1 III. lim 2

.

n 2n +n+2

n n +2n+2

n n +2n+2

1 a)f(x)= lim1x2n; b)g(x)= lim x2+ 2;

n n n