the fact, again (with a definition of e) | Summary and Q&A

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September 25, 2017
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blackpenredpen
the fact, again (with a definition of e)

TL;DR

The video discusses the fact limit and the definition of the number "e", providing algebraic explanations and examples.

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Q: What does the video call the limit (1 + alpha/x)^x as x approaches infinity?

The video calls it the fact limit, as it is a significant limit that will frequently appear in calculus.

Q: What is the definition of the number "e" presented in the video?

The video defines "e" as the limit of (1 + 1/T)^T as T approaches infinity.

Q: How is the fact limit related to the definition of "e"?

The video shows that the fact limit and the definition of "e" are equivalent by making a substitution and rearranging the algebraic expressions.

Q: Can the fact be used to evaluate other limits?

Yes, the video provides an example where the fact is used to evaluate the limit of (1 - 1/2x)^4x as x approaches infinity.

Summary & Key Takeaways

• The video introduces the fact limit for the expression (1 + alpha/x)^x as x approaches infinity, calling it the fact.

• The definition of the number "e" is also explored, using a limit expression (1 + 1/T)^T as T approaches infinity.

• By making a substitution and algebraic manipulations, the fact limit and the definition of "e" are shown to be equivalent.

• Examples are given to demonstrate how to use the fact to evaluate limits.