Use the graph, estimate the limit as x approaches -1.
The function f above is undefined for x=-1. By simplifying f(x) we find a function whose graph agrees with f(x) at every point except -1.
Since f(x) is undefined for x=-1 and we were able to cancel a common factor of x+1 from the numerator and denominator there is a hole in the graph of f(x) at x=-1
For f(x) to have a limit as x approaches -1 the one-sided limits must agree.
From the right:
From the left:
Since the one-sided limits agree, the limit exists.
Here are some practice problems.