Earlier on I showed what the direct substitution property is and how it can be applied to solve limits involving polynomials or rational functions very easily. In this video I go over a simple proof for the direct substitution property for polynomials using the limit laws, which I have also gone over in my earlier videos. In later videos I will provide precise proofs for all the limit laws used in this video.
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Direct Substitution for Polynomials: 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: