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Evaluating limits of compositions by looking at the limits of the innermost functions first, and then outer functions as they exist is particularly helpful when some of these limiting values are infinite. More generally, the limit laws can be used to show that the substitution rule is valid. Each can be proven using a formal definition of a limit

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We list some of them, usually both using. In turn, limit law (vi) implies that the substitution rule is valid for all rational functions tients of polynomials) In this section we will discuss the properties of limits that we’ll need to use in computing limits (as opposed to estimating them as we've done to this point)

This video focuses on finding the limit of composite functions, specifically the limit as 'x' approaches 'a' of f (g (x))

It explains that this limit equals f (limit as 'x' approaches 'a' of g (x)) if two. As it stands, this is not generally the. They are basically saying the same concept, i.e Convergence can be conveyed by composition when $f$ and $g$ both converge

As @ethan pointed out, the difference is. But, what about the limit of a composite function