will equal 0 if you apply the usual limit laws and consider the limit as t tends to -3 in the numerator.
Factorisation of the numerator and denominator gives us , which gives us the correct limit . However, I only know this because I looked at the graph.
It seems arbitrary that a simplification should produce a different result, if the expression is equal. How can I possibly tell whether a function has a limit at a particular point unless I do the "correct" manipulations? There must be some strict method I can apply to every function to ensure I know I am taking limits correctly.