Formal definition of limits Part 2: building the idea | AP Calculus AB | Khan Academy

Some background intuition to make the formal definition of a limit make intuitive sense. Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[linuxisbetter]

Yes! I'm taking analysis spring '13 and this is is going to be week 1. Please do more videos on proofs or

[rhoadess]

This |x-c|<δ and |f(x)-f(c)|<ε is very helpful in programing when you have a possibility for a floating point error. Computers can not be infinitely precise, so it is important to tell the computer at want ε or δ is sufficient for the task at hand. Another way to write it is abs(x-c)<δ and abs(f(x)-f(c))<ε

[Daski]

I've watched a bunch of videos about the topic and it's crystal clear to me that if the limit of f(x) is within epsilon of L, then x is within delta of a. I can visualize it, express it mathematically and it makes perfect sense, however, how does that prove a limit???

[jdmrchem]

Yes! A powerful video to understand the building of the idea of the epsilon-delta definition.

[blueunicolt]

Real life computers cannot be infinitely precise, but they can be arbitrarily precise, so long as they have sufficient memory to represent said precision.

[Dhyaneshwar-umln]

I don't understand, why being able to find a range around 'c' for any desired output range means the limit is true?

[TheBoBuilder]

"Loosey goosey" :'D That is all

[MsKTMvalley]

English major here. What's going on? lol :)

[Wolfie]

Integration by Parts + Tabular Method?