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[quote=Anonymous][quote=Anonymous]Even MIT doesn't use epsilon-delta in its definition of limit or proof of trig derivatives.

https://youtu.be/kCPVBl953eY?si=Qg67lEG7iQpkd74H
Lec 1-3

Calculus, whether it's IB, AP, or MIT, is a different class from Real Analysis [/quote]

Respectfully, you’re trying to prove a point without having the slightest clue about Calculus, it’s almost comical.

There’s a way to teach calculus rigorously using theorems, proofs and essentially derive as much as possible from first principles, which requires time and effort. Then  there’s the IB way where you just memorize and apply formulas because you’re cramming two semesters of calculus in two months.

For the example from MIT OCW to show the derivative of sin(x), the rigorous treatment is to start with the epsilon delta definition to prove the squeeze theorem. Then you use the squeeze theorem to show that limit of sin(x)/x is 1, which you use to show the derivative of sin(x) is cos(x). They go over that briefly in the prior video, and keep in mind that’s not the totality of the class content, there’s recitation, exercises and homework too.

At the lowly community college where my child took Calculus 1, they go over some form of epsilon delta and proof of sin(x) derivative. Even Khan Academy goes in more depth
https://www.khanacademy.org/math/calculus-1/cs1-derivatives-definition-and-basic-rules/cs1-proof-videos/v/derivative-of-sin-x
https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/v/sinx-over-x-as-x-approaches-0

I bet MIT does it too, they’ll teach the fundamentals and some more. Not in IB though because that would be fetishism. How about the rest, like teaching Calculus without the Fundamental Theorem of Calculus! Got it, that’s fetishism too, we can’t have that. Then you have some complete morons with the nerve to claim that IB goes in depth and does “analytical writing”, while AP is rote memorization and teaching to the test.

In all honesty if a child talented in math is made to take the IB route that’s bad parenting and teaching malpractice.

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