In this video I go through some useful examples in illustrating how to apply the limit laws which were discussed in my earlier videos. Also I introduce the direct substitution property which allows for directly solving limits of polynomial and rational functions. I will do more examples on cases where direct substitution does not apply in later videos so stay tuned!
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Limit Laws – Part 2 Examples: Plus “Direct Substitution Property”
Suppose that c is a constant and the limits below exist:
Called the Power Law
Examples: Evaluate the limits and justify each step.
Direct Substitution Property:
If f is a polynomial or a rational function and a is in the domain of f, then:
Functions with the Direct Substitution Property are called continuous at a. Not all limits can be evaluated by direct substitution, such as: