Limit Laws Examples + Intro to Direct Substitution Property

in MES Science2 years ago

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”

Limit Laws Part 2 - Examples Direct Substitution.jpg

Limit Laws:

Suppose that c is a constant and the limits below exist:

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Then:

Law 1:

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Law 2:

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Law 3:

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Law 4:

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Law 5:

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Law 6:

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Called the Power Law

Law 7:

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Law 8:

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Law 9:

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Law 10:

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Law 11:

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Examples: Evaluate the limits and justify each step.

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Direct Substitution Property:

If f is a polynomial or a rational function and a is in the domain of f, then:

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Functions with the Direct Substitution Property are called continuous at a. Not all limits can be evaluated by direct substitution, such as:

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