# How do you use a graph to show that the limit does not exist?

##### 1 Answer

Sep 27, 2014

Remember that limits represent the tendency of a function, so limits do not exist if we cannot determine the tendency of the function to a single point. Graphically, limits do not exist when:

- there is a jump discontinuity

(Left-Hand Limit#ne# Right-Hand Limit)

The limit does not exist at#x=1# in the graph below.

- there is a vertical asymptote

(Infinit Limit)

(Caution: When you have infinite limits, limits do not exist.)

The limit at#x=2# does not exist in the graph below.

- there is a violent oscillation

(e.g.,#sin(1/x)# at#x=0# , shown below)

I hope that this was helpful.