Love how excited you get when you solve a problem. Awesome.
@mscha3 ай бұрын
Note that you can also find solutions where u + v + w ≠ 6, so the premise is wrong. (Example: just replace ⁶√6 with ¹²√36.) The question should be something like: “Find u, v, w with u + v + w =6 such that ...”.
@PrimeNewtons3 ай бұрын
I agree.
@estanley01312 ай бұрын
One of my favorite videos of yours; the excitement building as you approach the solution and the flash when it becomes clear 10/10 would watch again
@darkemperor39463 ай бұрын
Hi Prime Newtons, I gave this question a try. I did show that u+v+w=6. But my working had a slight variation. Whereas you took the negative sign into the csc(6x), from "-csc(6x)" to csc(-6x)" ( which is also ok because csc is an odd function). I took the negative sign in the square root. Just like 4^(-1/2) = (-2)th root of 4, so is 6(-1/6) = (-6)th root of 6. Both methods prove u+v+w=6, only values of u and v change in each method. Just wanted to point this out. Appreciate your work!👍
@Samir-zb3xk3 ай бұрын
lol i did that too
@Jon609873 ай бұрын
Very nice problem and nice presentation. This is one of your best videos. Thank you!
@satyapalsingh4429Ай бұрын
You are a great mathematician .Keep it up !!!
@ukdavepianoman3 ай бұрын
Very nice solution. It looked slightly baffling at first...but following through the differentation steps it become clearer where it was leading. Nice trick to spot that the minus sign could go inside the csc function.
@kereric_c3 ай бұрын
NOTE that we can make sure that u = -6,however ,we could just find that w^(1/v) = 6^(1/6).for example there is a solution that w=36 and v = 12. in this condition u+v+w = 42
@Morgyborgyblob3 ай бұрын
I got to the top level of high school maths in Scotland, and did 1st year maths as an under grad at uni. I never encountered cosecent, cotangent, etc, until I went on youtube. It feels like a whole part of maths was just left out.
@nothingbutmathproofs71503 ай бұрын
Easy problem. As always, you did a great job in solving it!
@milko51432 ай бұрын
Amazing stuff
@ThePhotonMan1103 ай бұрын
Definitely required the biblical pasy after getting 666 at the end of the solution! Jokes aside, love the vids and your enthusiasm!
@mr.renovator48593 ай бұрын
Thanks for your great content! Keep it up. Like your very pedagogic explanations @ perfect speed!
@darcash17383 ай бұрын
Looked pretty weird to me at first, but I got it. f(x) = ln cot(3x)/ln6 f'(x) = 1/cot(3x) * -csc^2(3x) * 3 / ln6 = -1/sin^2(3x) * sin(3x)/cos(3x) * 3/ln6 = -3/ln6 * 1/sin(3x)cos(3x) = -3/ln6 * 1/(1/2)sin(6x) = csc(6x)/ (-1/6*ln6) = csc(6x) / (ln6^(-1/6)) = csc(6x)/ -6th root(ln6) 6 - 6 + 6 = 6 Not sure how you properly rewrite negative fractional powers, but that seems about right
@lucien3463 ай бұрын
It was beautiful the derivative can be simplified very easily
@rolandbole58243 ай бұрын
Check check check!!!! Love that.
@surendrakverma5553 ай бұрын
Excellent explanation Sir. Thanks 👍
@jennifertate43973 ай бұрын
Thanks man. Love your vids, and that you use a blackboard like when I was in school!
@vitotozzi19723 ай бұрын
What a amazing exercise!!!!
@trunks56143 ай бұрын
beautiful
@GURPARASSINGH-sg8sv3 ай бұрын
Hi sir ❤❤ First
@THN--ue2yn3 ай бұрын
I got 73/6. u=6, v=6, w=1/6. Instead of putting the negative sign inside cosec(6x), I put it inside the ln function.
@Harrykesh6303 ай бұрын
Easy !!!
@HasanOtoom3 ай бұрын
So satsfine❤❤
@robertcotton84813 ай бұрын
Csc(x)/(ln(1/6)^(1/6)) if put negative on bottom instead of top sums to 4/3
@robertcotton84813 ай бұрын
Added wrong 43/6
@THN--ue2yn3 ай бұрын
@@robertcotton8481 But it's 6x instead of x inside csc.
@robertcotton84813 ай бұрын
My point was that with the negative being able to go both up and down there is not just one sum
@THN--ue2yn3 ай бұрын
@@robertcotton8481 I know, when I did the sum I got 73/6 because I put the -ve sign inside the ln instead of csc.
@Reaper693773 ай бұрын
What will be the inverse function of f(x) = xe^x?? Someone slove please🙏🏻🙏🏻🙏🏻.
@5Stars493 ай бұрын
You win the race 😮
@pdfr3aderYT3 ай бұрын
why is w omega
@sammtanX3 ай бұрын
AMEN TO THAT
@Orillians3 ай бұрын
Can i get the source forr this question?
@shahadahmed72353 ай бұрын
Do you have any online courses?
@domedebali6323 ай бұрын
noice
@moeberry82263 ай бұрын
The problem can have more than 1 solution it is not necessarily the case that u and v and w have to be just 6 or -6.
@ppbuttocks20153 ай бұрын
The problem just asks to show the sum of these three numbers to be 6. It doesn’t matter the value of the numbers just the sum
@moeberry82263 ай бұрын
@@ppbuttocks2015 understood my point is the total sum changes, it is not the case that it’s always 6 that’s my point.
@omograbi3 ай бұрын
666 and so this problem has summoned the demon here
@temporarytemporary-fh2df3 ай бұрын
god forbids... this equation is fomented by the devil.
@slytherinbrian3 ай бұрын
Love the math, could do without the evangelism.
@PrimeNewtons3 ай бұрын
Thanks. I wish I could.
@true77813 ай бұрын
a) u + v + w = - 6 + 6m + 6ᵐ // u = -6, v = 6m, w = 6ᵐ b) u + v + w = 6 + 6m + (1/6)ᵐ // u = 6, v = 6m, w = (1/6)ᵐ 𝒇'(x) = csc(-6x)/𝒍𝒏(⁶√6) = csc(-6x)/𝒍𝒏(⁶ᵐ√(6ᵐ) = = csc(+6x)/𝒍𝒏(⁶√(1/6)) = csc(6x)/𝒍𝒏(⁶ᵐ√((1/6)ᵐ), m∈ℕ