Why you cannot always assume the limit of a composite function is f(L)
In short: Calculating the limit of f(g(x)) at a specific point requires more than just finding the limit of the inner function. This video explores the two essential conditions needed to ensure the math holds true.
To conclude that the limit of f(g(x)) as x approaches a equals f(L), two criteria must be satisfied: the limit of the inner function g(x) must exist and equal L, and the outer function f must be continuous at that value L. If either of these requirements is absent, the standard assumption fails.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Theorem for limits of composite functions: when conditions aren't met | AP Calculus | Khan Academy
To cite this card, link to https://intellectplus.co.uk/app/ideas-theorem-for-limits-of-composite-functions-when-conditions-ar.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
