In this video I continue further into the Direct Substitution Property for Limits and prove that it's true for rational functions while utilizing the same property for polynomials (which was proved earlier).
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Direct Substitution for Rational Functions: Proof
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: