Answer
Unbounded behaviour might occur for which the limit may fail.
Work Step by Step
When we graph the functions whose limit donot exist, we see that they increases without bound or reaches the infinity.
For example :
$f(x) = \frac{1}{x^{2}}$ have no limit.
we can see from the graph of f(x) that as x approaches 0 either the right or left side , f(x) increases without bound. This means that when we choose the value of x closes to 0, we will get f(x) to as large as required . Thus, the limit fails to exist.
Graph is attached below :
