Set the
table:
tbl start = 2 (the number x is getting
close
to).
D tbl = .0001
Look at the table and study
the y-values.
Coming from the left or
the right of x = 2 shows y = 7.
II. Use a graph of the function to find the same limit.
Graph the function and trace to x = 2. What is the y-value? 7
III. Use algebra and calculate the same limit. (Factor)
I. Use the table feature in a graphing calculator to find
Set the table: tbl start = 1 (the number x is getting close to).
D tbl = .0001
Look at the table and study the y-values.
Coming from the left or the right of x = 2 shows y = 5.II. Use a graph of the function to find the same limit.
Graph the function and trace to x = 1. What is the y-value? there is not one
Trace one pixel to the right and one pixel to the left to see it looks like it is getting
close to 5.III. Use algebra and calculate the same limit. (Factor)
Look at its graph, the table values, and do it algebraically by
making
it a piecewise function.
The reason this limit does not exist is because the limit as 
does not equal the limit
as 
.
when
The limit does not exist because the limit as 
is not equal to the limit as 
.
This
function
is unbounded as 
from
both sides.
This function continually oscillates more and more wildly
as
from either side.
