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Should I be concerned ?

Anonymous Tue 26 Oct 15:37:09 2021 No.13791942 View Reply Original Report

Quoted By: >>13791950 >>13792051 >>13792066 >>13792638 >>13792723 >>13792756

> be on Integral Calculus class
> learning about l'hôpital's rule
> the teacher has been marvelous so far.
> she uses l'hôpital on lim sinx/x
> \mfw

Anonymous

Anonymous Tue 26 Oct 2021 15:40:48 No.13791950 Report

Quoted By:

>>13791942
No, sin(x)/x is a good example for the 0/0 use case for LHP.

Anonymous

Anonymous Tue 26 Oct 2021 15:59:57 No.13792005 Report

Quoted By: >>13792637

op here
but isn't that just circular reasoning ?

Anonymous

Anonymous Tue 26 Oct 2021 16:16:36 No.13792051 Report

Quoted By:

>>13791942
Anon you're that guy in the class.

Anonymous

Anonymous Tue 26 Oct 2021 16:22:15 No.13792066 Report

Quoted By:

>>13791942
No, and consider the sanity check of the small angle approximation sinx=x in that limiting case.

Anonymous

Anonymous Tue 26 Oct 2021 19:57:05 No.13792637 Report

Quoted By: >>13792642

>>13792005
Why would that be circular? I don't understand what point you're trying to make, anon

Anonymous

Anonymous Tue 26 Oct 2021 19:57:12 No.13792638 Report

Quoted By:

>>13791942
Don't think about if you should be concerned or not. Do not judge your teacher, just learn from them whatever you can.
btw I hate teachers that aren't rigorous.

Anonymous

Anonymous Tue 26 Oct 2021 19:58:32 No.13792642 Report

Quoted By: >>13792664 >>13792691

>>13792637
the derivative of sinx is computed through the use of exactly that limit. So it is not the best way of computing it.

Anonymous

Anonymous Tue 26 Oct 2021 20:03:11 No.13792664 Report

Quoted By: >>13792695

>>13792642
>the derivative of sinx is computed through the use of exactly that limit. So it is not the best way of computing it.
If you directly define sinx via trigonometry. You can define sinx via taking Im(e^ix), show that it does parameterize the unit circles imaginary part lengthwise and then l'hôpital rule application is valid.

Anonymous

Anonymous Tue 26 Oct 2021 20:07:20 No.13792691 Report

Quoted By:

>>13792642
Ah. Well, that depends on how you choose to define sin(x) and cos(x). Personally, I'd prefer the Maclaurin series definition: sin(x) = x - x^3/3! + x^5/5! - ... . Of course, then you don't need L'Hopital's rule becaus you can divide out x termwise (actually, iirc something like that might be where L'Hopital's comes from? I think it's just from the Taylor expansion or something).
But the point is, it's a perfectly fine example if you come in with "the derivative of sin is cos, derivative of cos is -sin" as known knowledge (that you may have solved using L'Hopital's, or not -- again, series works, or maybe you chose to define sin and cos using their derivative identity and derived their other properties -- or, idk, fuckin empirical measurements, idc) and want to compute the limit.

Anonymous

Anonymous Tue 26 Oct 2021 20:08:57 No.13792695 Report

Quoted By:

>>13792664
>If you directly define sinx via trigonometry. You can define sinx via taking Im(e^ix), show that it does parameterize the unit circles imaginary part lengthwise and then l'hôpital rule application is valid.
And in fact this is simpler than actually doing axiomatic geometry to get to trig functions and equally rigorous. In fact, doing axiomatic geometry in a way that allows you to develop analysis is fucking annoying and noone does it, so the easy way is to just start with the real and complex numbers and do everything analytically, defining sinx as the imaginary part for e^ix.

Anonymous

Anonymous Tue 26 Oct 2021 20:15:32 No.13792723 Report

Quoted By:

>>13791942
In any case, anon, the real answer is that if you want that level or rigor, you should go take an analysis class, not expect it in your calculus classes. Calc teaches you to apply useful things like limits, derivatives, integrals, paths/volumes, series, etc. Analysis (real and/or complex) teach you how to start from axioms and actually reach rules like L'Hopital's. If your Calc class isn't perfectly rigorous, it's because they've got a shitload of idiots to teach Calc to, and it's more efficient to teach things in an almost-rigorous way rather than raising points (that the idiots won't understand anyways) every time they gloss over technical details.

Anonymous

Anonymous Tue 26 Oct 2021 20:23:56 No.13792756 Report

Quoted By:

>>13791942
you're lucky enough if you get an instructor who can speak intelligible english, they don't need to know math, thats what the textbook is for.

Anonymous

Anonymous ## Mod Tue 26 Oct 2021 20:35:18 No.13792806 Report

Quoted By:

This thread was moved to >>>/r9k/65910952

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