You can have various types of functions and various behaviours as they approach zero;
for example:
1] f(x)=1/x is very strange, because if you try to get near zero from the right (see the little + sign over the zero):
lim_(x->0^+)1/x=+oo this means that the value of your function as you approach zero becomes enormous (try using: x=0.01 or x=0.0001).
If you try to get near zero from the left (see the little - sign over the zero):
lim_(x->0^-)1/x=-oo this means that the value of your function as you approach zero becomes enormous but negative (try using: x=-0.01 or x=-0.0001).
2] f(x)=3x+1 as you approach zero from the right or left your function tends to 1!
lim_(x->0)(3x+1)=1
Basically, as a general rule, when you have to evaluate a limit for x->a try first to substitute a into your function and see what happens. If you get something problematic such as 0/0 or oo/oo or 1/0 try to get as near as possible to a and see if you "see" a pattern, a trend...a tendency!
