Can you always find the limit of a composite function?
In short: Calculating the limit of f(g(x)) isn't always straightforward. This video explains the specific mathematical conditions required to safely evaluate the limit of a composite function using the limit of its inner component.
To determine the limit of f(g(x)) at a specific point x=a, you can only assume the result is f(L) if two criteria are met. First, the limit of the inner function, g(x), must exist at x=a and equal L. Second, the outer function, f, must be continuous at that resulting value L. If either condition fails, the standard substitution method cannot be assumed to be valid.
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Sources
- Summary by Intellect · source: Theorem for limits of composite functions | Limits and contiuity | AP Calculus | Khan Academy
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