Great question with a mind blowing explanations!!! Never thought a solution could be made by forcing it and that it could be approached this way... Thanks Sir!!
Explanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.
Prove this following : if the bases are in arithmetic progression, and the exponent, n, is odd; then the expression is divisible by the sum of the bases. Written mathematically: [ a^n + ( a + d )^n + ( a + 2d)^n + ........ + ( a + ( r - 1 )*d )^n ] is divisible by r* [ 2a + ( r - 1 )*d ] / 2.
Explanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.
if k>2034 then AUC of the curve is bigger than sqrt(8) (because the function is strictly increasing in respect of k). So 2034 is the largest possible value of k
Right, the function is given, so this manipulation gives the solution. My question was dumb. Thanks, anyway. But should 2034 then not be also the only solution?
Very very well explained. Easy step by step approach, awesome!
Very tricky and nice solution.
I guess this should be the most elegant solution. Beautiful. :)
Why is it 2n minus 1 equals 2018 minus n..those arent the same,exponent..
What a beautiful problem,and how simple logics are used too,great,thank you sir..
Great question with a mind blowing explanations!!!
Never thought a solution could be made by forcing it and that it could be approached this way...
Thanks Sir!!
Well, I'm proud I at least tried this one. It was quite interesting; I would love a problem similar to this in the future.
Amazing! Hey but what about that work done by spring analogy somebody did in the comments, I would like to know more about that!
Wasn't the problem originally asking for "all possible values of k?"
Nicholas Patel,,, How did you solve this??
Great solve!!!!!
this guy is a mad genius
Can I please know,what degree did u get
Why is k the largest possible?
Does he write on with a pen of sorts or does he just use a mouse?
What Is The App he use ?
Interesting stuff!
Your accent sounds little bit like blackpenredpen XD
lol agreed
His accent sounds similar *isn't it?*
Not at all, in my opinion
not even close mate
Goodness!
Mind blown
I tried both methods of Usub. Then thought I can try to make it its derivative and use that...though didn't know how. Thanks
Super!!
Dear sir how did you justify that only one case is possible square root of 8 . Could you please shed light onto it!
Explanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.
Can you upload more tricky u sub
Prove this following : if the bases are in arithmetic progression, and the exponent, n, is odd; then the expression is divisible by the sum of the bases.
Written mathematically:
[ a^n + ( a + d )^n + ( a + 2d)^n + ........ + ( a + ( r - 1 )*d )^n ] is divisible by r* [ 2a + ( r - 1 )*d ] / 2.
I knew my explanation was pretty close.
K no puede ser negativo también?
Isnt it +-sqrt(8)?
Explanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.
I love this so much
Why is 2034 the largest possible value of k?
if k>2034 then AUC of the curve is bigger than sqrt(8) (because the function is strictly increasing in respect of k). So 2034 is the largest possible value of k
Right, the function is given, so this manipulation gives the solution.
My question was dumb.
Thanks, anyway.
But should 2034 then not be also the only solution?
The integral evaluates to -sqrt(8) for another value of k. That value is approx -6091.9754
@@jiaming5269
Ah, ok.
Magic!
Thanks
❤❤ :)
Thanks you
زين العابدين ماجد
يلحبيب
Thanks you
او
Thank you
هاي for اشطبها بعد اذن شواربك
@@yassarmandouri3221
هههههه صار
Do you remember to put your socks on before your shoes?
First
Just wtf man
second
"Nicholas Patel", huh, an "h" like me... you copycat ! (; p)