How do you use a graph to show that the limit does not exist?
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
The limit does not exist at
#x=1#in the graph below.
- there is a vertical asymptote
(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
#sin(1/x)#at #x=0#, shown below)
I hope that this was helpful.