What is the limit of #f(x)# as #x# approaches 0?

Question

Sadie Alexander · Accepted Answer

It depends on your function really.

As they get closer to zero, you can have different kinds of functions and different kinds of behaviors; for instance: 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!

Sadie Alexander · Answer

undefined To determine the limit of $ f(x) $ as $ x $ approaches 0, you would need to know the function $ f(x) $. Without knowing the specific function $ f(x) $, it's impossible to provide a precise answer. Limits are dependent on the function's behavior as $ x $ gets closer and closer to a particular value, in this case, 0. So, you would need to provide the function $ f(x) $ in order to calculate the limit as $ x $ approaches 0.