Limits
Practice
Below are scrambled practice problems incorporating each method of solving for limits.
4.1 
4.2 
4.3 
4.4 
as seen graphically
4.5 
as seen graphically
4.6 
4.7 
Does not exist as seen graphically
4.8 
Since both function approach 1 we have a limit at 1
4.9 
4.10 
4.11 
4.12 
In conclusion:
A limit is a y value.
One-sided limits always exist
A limit does not exist only when a function is discontinuous.
A limit can always be found graphically, whether it’s solving, factoring or asymptotic. On exams when you are given the use of a graphing calculator, it’s always a good idea to check your work by solving for the limit graphically as long as you have time.
