/sci/ - Science & Math

[Anonymous No.9924834]

Can people on this fucking board post some real math for once

[Anonymous No.9924850]

OK you begin.

[Anonymous No.9924922]

How about a starting topic?
Can you explain, in detail, Maxwell's Equations?

[Rick No.9924947]

FUCK YOU I WILL EXPRESS IRRATIONAL VALUES IF I DAMN WELL PLEASE!!

[Anonymous No.9924957]

>>9924834
>[math]log[/math]
>not [math] \log [/math]

[Anonymous No.9924975]

>>9924922
>Maxwell eqns
NEXT

seriously tho what do you wanna know?

[Anonymous No.9925038]

Exercise for fellow calculuslets. Solve the following *without* resorting to L'Hospital's rule. Explain how you solved it, or I'll suspect you cheated and used L'Hospital's rule.
(If you can do it in your head in less than 15 seconds, the question isn't for you.)
[math]\lim \limits_{x\to 0}{\tan(3x)\over \sin(8x)}[/math]

[Anonymous No.9925106]

>>9925038
[math]

\frac{tan(3x)}{sin(8x)} = \frac{tan(3x)}{sin(8x)}\frac{3x}{3x} = \frac{sin(3x)}{sin(8x)}\frac{3x}{3x}\frac{1}{cos(3x)} = \frac{sin(3x)}{3x}\frac{8x}{sin(8x)}\frac{1}{cos(3x)}\frac{3}{8} \rightarrow 1\cdot 1\cdot 1\cdot \frac{3}{8} = \frac{3}{8}
[/math]

since trivially

[math] \frac{sin(y)}{y} \rightarrow 1 \leftarrow \frac{y}{sin(y)} [/math]

and [math] cos(x) [/math] is continous at 0.

Anyone who needs to use L'Hopital for any limit is the definition of a brainlet and has no chance in academia.

[Anonymous No.9925149]

>>9925038
>>9925106
cont. and since you're such a good sport and gave me 15 seconds to solve it, I'll return the favor, but to make things fair I give you 30 secs since mine is harder.

Tell me if the function

[math]

f(x,y) = \begin{cases}
\frac{x^{5}y^{2}}{x^{8} + y^{4}} & \text{for } (x,y) \neq (0,0) \\
0 & \text{for } (x,y) = (0,0)
\end{cases}

[/math]

is continous at the origin.

People who think they know real analysis can apply too, but don't get your hopes too high, fellows.

[Anonymous No.9925154]

>>9925106
Good answer.
>Anyone who needs to use L'Hopital for any limit is the definition of a brainlet
Probably correct, but L'Hopital sure makes a lot of limits that would otherwise require effort trivial.
For example, you can use it to instantly verify that sin(y)/y -> 1 as y->0, instead of actually having to think and produce a geometric proof.

[Anonymous No.9925161]

>>9924834
[math]2\times 3=6[/math]

[Anonymous No.9925206]

>>9925149
With the AM-GM inequality it's easy to see that
[eqn]\frac{x^4}{y^2} + \frac{y^2}{x^4} \geq 2 [/eqn]
Using that we get
[eqn]
\left| \frac{x^5 y^2}{x^8 + y^4} \right| = \frac{|x|}{\frac{x^4}{y^2} + \frac{y^2}{x^4}} \leq \frac{|x|}{2} [/eqn]
So it's continuous in the origin.

[Anonymous No.9925234]

>>9925206
>continuity of absolute value implies continuity

A fatal mistake, my friend. Consider sgn(x), which isnt continuous at origin, but abs(sgn(x)) = 1 obviously is, I advise you to try again with a more distinguished approach. I can give you one hint if youd like.

[Anonymous No.9925282]

>>9925234
>continuity of absolute value implies continuity
Nobody implied that but
f(x,y) -> c is equivalent to |f(x,y) - c| -> 0
Here c=0.

[Anonymous No.9925350]

>>9925154
Nigga, you can't use L'Hospital rule for sin(y)/y, it's circular logic.

[Anonymous No.9925375]

>>9925350
>prove L'Hospital's rule
>apply it to sin(y)/y

[Anonymous No.9925396]

>>9925375
The definition of the derivative at 0 of sine function is the limit
[eqn] \lim_{y \to 0} \frac{\sin(y)}{y}[/eqn]
To apply l'Hospital's rule here you need to know the derivative of the sine function.

[Anonymous No.9925405]

>>9925396
OH. I just jumped in randomly to this conversation and had not considered that. Carry on.

[The Lord No.9925414]

[Anonymous No.9925441]

>>9925396
>To apply l'Hospital's rule here you need to know the derivative of the sine function.
But I do know the derivative of the sine function. So, you could argue that applying L'Hospital's rule makes no sense. But actually, it's not mathematically incorrect, it's just redundant and arguably stupid - I'm considering the derivative as a given, and then using a roundabout method to use that derivative to calculate itself.
That's the nice/annoying thing about L'Hospital's rule, depending on whether one is a brainlet - you can memorize some identities and derivatives and then brute force your way through a bunch of limits without understanding wtf is going on.

[Anonymous No.9925460]

Why isn't latex rendering? I'm fucking retarded I can't remember how to get it to render.

[Anonymous No.9925467]

>>9925460
Turn off adblock/ublock. It is blocking the cross-domain script request that enables latex iirc.

[Anonymous No.9925474]

>>9925467
Also it might be enough to whitelist requests to mathjax.org if you don't want to fully disable your adblocker, but that will depend on your particular extension and how it works

[Anonymous No.9925512]

>>9924834
There isn't logic or proper math in whatever the fuck you think you're posting.

[Anonymous No.9925518]

>>9925396
That's literally not the definition of a derivative. Go read a book, preferably not a mathematics one, go find one you can understand.

[Anonymous No.9925530]

>>9925518
He said the derivative at x=0.
So derivative of sin(x) is lim (y->0) of [sin(x+y)-sin(x)]/y
At x=0, the sin(x) term is 0, and sin(x+y) is sin y.
That gets us lim y->0 of sin(y)/y.

[Anonymous No.9925531]

>>9924834
THANKS FOR THE EXERCISE I WILL NOW TAYLOR THE HECK OUT OF THESE SO THAT I CAN REMEMBER FOR LIFE HOW TO EXPAND A LOG INTO A FAGGOT

[Anonymous No.9925535]

>>9925530
Yeah, just like taking an integral, we plug in the bounds before taking the integral...

[Anonymous No.9925548]

>>9925149
might be too facetious but i'll bite
8 > 7 so that graph is going nowhere near 0 , i'd say isn't

[Παρόν No.9925559]

>>9924834
Oh hey, Πολυωνυμιkή Δυνάμεις Προ-ανίχνευση
>"Πολυωνυμιkό χρόνο Κατηγορηματιkή Δυνάμεις"

[Παρόν No.9925563]

>>9925149
Yes, if the origin is Π or π

[Anonymous No.9925577]

>>9925548
As you approach along the line y=x, you get x^7/(x^8+x^4) =
x^3/(x^4+1)
As you get closer to 0, the numerator approaches 0, the denominator rapidly approaches 1, and the limit is 0.
If you approach along the x or y axis, you also get 0.
So the value can clearly go to 0 as x,y->0.
(this doesn't mean that 0 is actually the limit though.)

[Anonymous No.9925583]

>>9925038
>>9925106
>>9925149

Wow so much edge there boys, calm down.

[Παρόν No.9925587]

>>9925583
https://www.wolframalpha.com/input/?i=c%5Cpi%2Ffloor(x+%2B+y+%2B+z)%5E-3+%2B+w%5Cpi%2Fabs(x+%2B+y+%2B+z)%5E2+%2B+v%5Cpi%2Fceil(x+%2B+y+%2B+z)%5E3+%2B+i+t

[Anonymous No.9926342]

>>9925577
thanks for explaining, it means much to me.

[Anonymous No.9926350]

>>9924834
I rather post my YuGiOh cards collection

[Anonymous No.9926372]

I'm sorry my good fellow. It seems you have misunderstood the purpose of this web forum. This site, or rather this part of the site, is for the discussion of SCIENCE related topics. Unfortunately the topic you suggested, 'real' mathematics does not fall under the science umbrella. Perhaps you would prefer this sub forum instead, >>>/b/.

[Anonymous No.9926382]

>>9926372
this pretty much

[Anonymous No.9926748]

>>9924975
I WANT REDDIT OUT!!!!

[Anonymous No.9926754]

>>9926342
>Bulbasaur used vine-touch
>it's super effective!
>Squirtle died!

[Anonymous No.9926855]

>>9926372
/sci/ - Science & Math

[Anonymous No.9926874]

prove FLT

i tried to read the paper but can't understand anything, category, scheme, math symbols I don't know how to google.

[Anonymous No.9927169]

>>9926874
If you want something interesting, look up Cherenkov radiation, but please don't apply this beyond the scope it is intended.

[Anonymous No.9928073]

>>9925038
Kind of lazy and in bed so I'll just describe what to do.
Power series of tan3x over power series of sin8x
L'H rule is really just a quick version of doing all the power series shit, if you rememeber back to calc 1 and early 2 definition of integrals being series and shit.