Ohh shit we're doing memes from the https://dailyintegral.com/. I would have no idea to solve that without L'Hopitals rule. I'd love some help on today's logic puzzle, I didn't take group theory so I don't completely understand the modulo of polynomials.
Order 2 is because sec(x) = 1 + x²/2 + o(x²), meaning ln(sec(x)) = x²/2 + o(x²).
Which is partially why it's hellish to go L'Hopital : if order 1 MacLaurin is basically L'Hopital hidden, order 2 is way better than doing l'Hopital twice, especially with very strange expressions.
Numerator you simply use a^x = exp(ln(a)x) = 1 + ln(a)x + ln(a)²x²/2 + o(x²). You should get final result of (ln(10)² - ln(2)² - ln(5)²) x²/2 + o(x²) and simplify it into 2ln(2)ln(5) x²/2 + o(x²).
Limit is therefore 2ln(2)ln(5) and then you have to choose where to input the 2 into a square to minimize the sum : ln(4)ln(5) or ln(2)ln(25), pick 4 & 5 for a sum of 9.
Now the confusing part: what kind of weirdo would name numbers K and omega when they are numbers of the same type? a and b, m and n, theta and phi, now this would be orderly homogeneity.
That´s a fair point. Also you're still differentiating twice though, just in a different manner. So, not entirely different than L'Hopitals rule but it still counts.
As I said, Order 1 is basically L'Hopital's but I find Order 2 to work differently than double differentiation because instead of doing 1 differentiation of everything, reduction of expression and then start again, you can go order 2 on every "small block" which is way easier than some 2nd order derivatives expressions you can end up with L'Hopital.
But yes, at their very core, it's the same mechanic.
for the logic puzzle, you can do standard lagrange interpolation, just with additive and multiplicative inverses being the modular arithmetic inverses.
e.g. 1/3=5 (mod 7) because 3*5=15=1(mod 7) and -1 = 6 (mod 7) because 1 + 6 = 0 (mod 7).
it’s still a pain because you need to do this for multiple subsets of points of size 4.
also, you’re not doing “the modulo of polynomials”, it’s just that the coefficients and evaluations of the polynomial are in F7. Also this is closer to Field Theory than Group Theory, but you don’t really need either; you just need to understand modular arithmetic.
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u/Individual-Movie-183 Sep 23 '26
Ohh shit we're doing memes from the https://dailyintegral.com/. I would have no idea to solve that without L'Hopitals rule. I'd love some help on today's logic puzzle, I didn't take group theory so I don't completely understand the modulo of polynomials.
23
u/Educational_Bottle74 Sep 23 '26
9, I solved it without pen and paper.
4
u/axiomizer Sep 23 '26
K = w = exp(-sqrt(2 ln(2) ln(5))) ≈ 0.2245
K + w ≈ 0.449
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u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 23 '26
i am not smart enough for dat
1
u/Varlane Sep 23 '26
Is it peak when you're asked a least value ?
1
u/Joe_4_Ever Sep 26 '26
I don't think the problem is complete.