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!