Theorem: Calculus is wrong.
For a theory or set of knowledge to be true, it must always give correct results. A failure to do so, at even an instance, invalidates it and will require a reformulation of the theory and procedures.
That said. Lets get the derivative of sinx.
Easy, right?
(sin(x+h) - sin(x))/h as h->0
(sin(x)cos(h) + cos(x)sin(h) - sin(x))/0 as h-> 0
because h->0, cos(h)->1 and sin(h)->0
(sin(x) - sin(x))/h as h->0
so we end up with
0/h as h->0 which is basically 0/0, that is to say undefined.
Therefore, our current calculus FAILS to get a defined derivation of sine, and you will see that the same thing happens for cosine.
Therefore all of calculus is wrong and you are all basically morons for studying so much of it when it was all wrong. All you had to do to prove it was to try to derivate sin or cos and realize that some faggot 300 years ago called Isaac Bumfuckton just made up the derivative and paid no close attention to that would happen.
Q.E. Motherfucking D.
>>7871037
kek
>>7871037
(You)
>>7871037
>i'll take the limit of sin and cos but forget to take the limit of h in the same expression
is this the new 1 = 0?
>>7871037
There is so much wrong here, let's make sure it stays on the first page so everyone gets a chance to laugh
>>7871050
>>7871053
Still doesn't invalidate my point.
WHY CAN'T WE FIND THE DERIVATIVE OF SINE AND COS THROUGH THE DEFINITION OF A DERIVATIVE?
It makes no sense. Derivatives are rigorous huh? That is what you may think but if it was then the definition of the derivative would never fail to give a correct result.
>>7871059
>why can't we
you mean why can't YOU find it. everyone else has no trouble with it, genius. you can't take the limit as h->0 by evaluating h=0 in part of the expression and then acting surprised when shit comes out.
>>7871059
What is the Taylor series?
>>7871097
what the fuck does taylor series have to do with the derivative of sin? what you need for this is lim sin(x)/x and lim (1-cos(x))/x.
of course if you have the theory of taylor series and you prove that for any convergent taylor series the sum of derivatives of each term converges to the derivative and you have the definition of sin and cos as taylor series then you have the result as well, but that's using a fucking bomb to move a stone
Ooooo, this thread looks interesting!
>>7871059
If you seriously aren't bullshitting us, then here
>https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx
>>7871113
>theory of taylor series
This is literally the definition of the sine function. Absolute convergence admits its "term-by-term" differentiation and every element of the underlying sequence is a power function so it's pretty simple.
Using identities on sin(x+h) always feels backwards to me, especially since you usually prove the angle sum identities from euler's identity, which depends itself on understanding what exp, sin and cos are, rigorously speaking. Because otherwise what the fuck does complex exponentiation even mean to you?
But, ah, the joy of engineering students.
>>7871037
bump for blurry akari
>>7871140
it's "pretty simple" but you already had to talk about absolute convergence and an absolutely convergent series admitting term-by-term differentiation. so clearly not "pretty simple". coming out here and trying to act smug does no one any good. we're talking about a first course in calculus, these topics aren't fit for that.
>>7871155
0/10
>>7871155
It isn't any damn contrived bullshit, we've got basic laws of trigonometry, and the squeeze theorem to prove that lim[(sin(x))/x] as x->0 is 1.
If we had no fucking idea what calculus was, those would still be true. If you don't wanna accept this shit, then start from the beginning and prove that you're even allowed to divide real numbers in the first place
>>7871149
Well, then maybe analytic functions just aren't for a first course in calculus. Those would be your words though, not mine.
If it's the type of course to present a "proof" of the derivative of sine that simply assumes that identity, why not simply assume it's true outright? Especially since their graphs make it seem intuitively plausible if that's all you're going for.
>>7871037
Ever heard of L'Hopital's rule?
>>7871205
>intuitively plausible
what are you talking about? lim sin(x)/x is done by the squeeze theorem between 1 and cos(x)
>>7871209
No, but I've heard of L'Hôpital's rule. XD
>>7871213
He was responding to the guy talking about using taylor series
>>7871213
Lets go back to >>7871205
>assumes that identity
What identity? Well, let's try >>7871140
>Using identities on sin(x+h) always feels backwards to me, especially since you usually prove the angle sum identities from euler's identity
That term of course comes up when you're proving its derivative is cosine from the definition. In the first line
>>7871225
elementary introductions to complex numbers and euler's identity do not use the definition of e, sin and cos as power series. they use geometric results from the definition of sin and cos as triangle ratios. there is, in fact, a simple geometric proof of the angle sum formula by triangle constructions
>>7871225
also, you're a real faggot for being incredibly unclear and acting smug when you're misunderstood. "that identity" my ass, there's quite a lot of identities being used when differentiating sin
>>7871037
I'd declare this thread to be a /sci/ cringe thread, but 90% of /sci/ is cringe-worthy anyways, so there's not much point in that.
So I guess have fun racking up all these (You)s from the autists of this board that feel the need to argue with a blatant troll. 10/10, 200 replies guaranteed.
>>7871214
Uhmmmmm I've heard of the hospital rule, it says you're gonna end up there if you stay memeing like that buddy, better watch your back ;)
>>7871247
>hurr im gonna beat you up
brutum fulmen, niger
>>7871241
>being incredibly unclear and acting smug when you're misunderstood
lolol wow
Yeah I get it, you don't have the barest responsibility to understand what I'm saying or even so much as go back through the thread to find out. To whatever extent you misunderstand, it's entirely my fault.
You are going to have SO MUCH FUN in math
Taylor Series is fucking magic. once you take numerical methods, you never analytically solve anything ever again. Taylor series that motherfucker and chop off the higher order terms in a super handwavy "order of error term".
Navier Stokes - Taylor Series
Heat Diffusion Equation - Taylor Series
its all bullshit m8.
>>7871282
yes
>>7871050
>i'll take the limit of sin and cos but forget to take the limit of h in the same expression
So what? This changes nothing.
Lets the the limit of x^2 + x as x->0 or whatever.
x^2 + 0. Here I take the limit of x, but not of x^2
0 + 0 = 0.
See? I took the limits one step at a time and that changed nothing. It is perfectly reasonable to take the limits of some parts, while leaving others for the next step.
sin(x+h) - sin(x) / h
= cos(x)sin(h) + sin(x)cos(h) - sin(x) / h
= sin(x)(cos(h) - 1) + cos(x)sin(h) / h
the first term goes to zero
sin(h) = h as h -> 0
cos(x)h / h = cos(x)
>>7871037
More like not even wrong
>>7871037
[sarcasm]Why aren't you putting this in a paper instead of 4chan? It's not like you have shitty math skills and will instantly get BTFO by people that have actual math skills. [/sarcasm]
>>7871268
>are going
been here for years friend. im sure you dont have many friends with that faggot smug attitude of yours.
>lololol wow + passive aggressive sarcastic shit
are you 12
>>7871569
>This changes nothing! See? Here's an example where nothing changes! :^)
nice bait
>>7871037
>>7871037
You might be onto something. I was looking at something the other day... I had put 0/0 into my calculator and it said UNDEFINED! What?!?! I had returned the calculator to Walmart as defective and had it replaced. With my new calculator I tried again... 0/0 and it said UNDEFINED again!!
Well, went to my maths teacher and she said its supposed to say that?!
Wow, these maths people are really stupid. I mean, if dividing can't be done that makes almost every "theory" of theirs false!
Thankfully my intelligence has saved me from their dogmatic indoctrination attempts, but there needs to be more of us being vocal about this! We need to rally people and put an end to this racist social construct "mathematics" once and for all!
>>7872573
Absolutely agree. The other day I failed a test because the prof didn't recognize that his cancellation rules don't work. I said that the limit of (log n) / n can be solved by moving the log outside and cancelling so [math]\frac{\log n}{n} = \log \frac{n}{n} = \log 1 = 0[/math] and even when I got the correct result he failed me.
>>7871037
Use the fucking Tex, reading equations like that hurts my eyes.
>>7871037
>Lets get the derivative of sinx
cosx.
q.e.d
>>7871037
Try looking at the proofs when it comes to differentiation and you'll find that because we can't divide by zero, we use a very small number. This imperfection is not a fault. There are lots of little blips in maths, don't pick on them - they make it beautiful!
>>7871037
If calculus is wrong how do you know what a derivative is and that the sine function has one?
checkmate atheist
>>7872676
>moving the log outside
>evaluating n/n inside the log
10/10 underrated post full of subtext
1/x = x/1
x^2=1
lim 0->inf 1/x=x/1
0 = inf
0^-1 * inf = 1
Qed
Directed to: >>7871037
>>7872735
>I don't know how to evaluate a limit
>therefore all of calculus is wrong
blimey this is some good shit in here
pic distantly related
>1 = x/x
>x->0 as x->0 so x/x -> 0/x as x->0
>but then 1 is undefined!
At last I truly see. Numbers don't exist. Math is a lie!
>>7874693
Sin(1/x) is continuous about 0...?
Did you know that
sin(1/x) is not derivable although it is continious in every point?
That's because left- and right derivate in every point has no limit.
[math]\frac{1}{x}\to\infty \space when\space x\to0[/math] thus
[math]\lim \limits_{1\to\space+\infty} \operatorname{sin}\frac{1}{x}[/math] and [math]\lim \limits_{1\to\space-\infty} \operatorname{sin}\frac{1}{x}[/math] has not limit and that is why for every x [math]\operatorname{sin}\frac{1}{x}[/math] is not derivable
>>7874777
ok, fuck this shit. on 4chan's TeX preview it worked fine, but when i post it goes bogus. UGH
>>7874782
[math]\lim \limits_{1\to\space+\infty} \operatorname{sin}\frac{1}{x}[/math] and [math]\lim \limits_{1\to\space-\infty} \operatorname{sin}\frac{1}{x}[/math] has not limit and that is why for every x [math]\operatorname{sin}\frac{1}{x}[/math]
[math]\lim \limits_{1\to\space+\infty} \operatorname{sin}\frac{1}{x} \space and \lim \limits_{1\to\space-\infty} \operatorname{sin}\frac{1}{x}[/math] has no limit and that is why for every x sin(1/x)) is not derivable.
>>7871037
Gödel
>>7871037
Derivate is not a verb. Were you trying to say derive or is derivate your Ebonics version of derive? Let's conversate.
>>7874777
>continuous, but not differentiable at a single point
Small time
