Why odd powers create divergent paths at infinity
In short: Understanding limits at infinity requires looking past the surface of a function to its dominant behavior. This video explores how odd powers in quotients dictate different results for positive and negative infinity.
The video demonstrates how to evaluate limits at infinity for quotients involving square roots, specifically focusing on expressions where the leading term is raised to an odd power.
Using the example of x / sqrt(x + 1), Sal Khan explains that because the leading term's exponent is odd (1), the function approaches different values as x moves toward positive versus negative infinity.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Limits at infinity of quotients with square roots (odd power) | AP Calculus AB | Khan Academy
To cite this card, link to https://intellectplus.co.uk/app/ideas-limits-at-infinity-of-quotients-with-square-roots-odd-power-.
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?
Related
More in Mathematics · More in Ideas & Philosophy · Latest · A–Z · All topics
