Conceptual Idea of a Limit
Example:
Left-hand limit: We say that the limit of f (x) as x tends towards c
from the left is L if f (x) is very close to L whenever x is very close
to, but less than, c.
1
lim  
x 0  x
This is denoted by:
lim f ( x)  L
xc 
Right-hand limit: We say that the limit of f (x) as x tends towards c
from the right is L if f (x) is very close to L whenever x is very
close to, but greater than, c.
1
lim  
x0 x
This is denoted by:
lim f ( x)  L
x c 
The limit: We say that the limit of f (x) as x tends towards c is L if
f (x ) if the left-hand and right-hand limits exist and are both equal
to L.
This is denoted by:
lim f ( x)  L
1
x0 x
lim
Does Not Exist
x c
Note: Later, we will make this idea more formal by more rigorously specifying what we mean
by “tends toward” and “very close”. We will want to specify that f (x) is arbitrarily close to L
whenever x is close ‘enough’ to c.