Understanding Continuity for a Function with Variable n

[transgalactic]

i added a link with the picture of the solution
i can't understand a certain solution
of finding for which values of "n"
he function is continues

first they split n<0 case
and check what limit comes out of it
an get that the limit is not constant so it not possible

then they check n>0 case
and get a constant limit value and then suddenly they switch
to the answer n>=1
how did they get this answer?

why in the first place they picked the case n>0
n<0

why couldn't i pick the cases
n>9
n<9

why did they pick this number??

http://img337.imageshack.us/my.php?image=66816873ds0.png

 

[Shooting Star]

They are considering n as an integer; so n>0 => n =1 or n>1.

The reason they did not pick n > or < 9 is because the general characteristic of the function is the same for, say, n=7 and n=10 at x=0. The properties change when n crosses over from positive integral values to zero or negative integral values.

Have you understood why it's continuous at x=0 for positive integral values of n? (You've already understood the situation for negative n, you said.)