Advanced Olympiad Integral Calculus
7:38
7 сағат бұрын
Пікірлер
@user-ee7nw2rx9s
@user-ee7nw2rx9s 2 күн бұрын
Это уже третий человек который решает этот пример
@DommarajuJyothi
@DommarajuJyothi Күн бұрын
👍
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 6 күн бұрын
Great work🎉
@DommarajuJyothi
@DommarajuJyothi 6 күн бұрын
Thank you 🙏
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 12 күн бұрын
Well said🎉
@DommarajuJyothi
@DommarajuJyothi 12 күн бұрын
Thank you
@herbertwandha6110
@herbertwandha6110 13 күн бұрын
Firstly,I commend you for this good job you do teacher to many out there. In the resulting cubic equation ,the splitting of term + a in terms of -36a and -37a in relationship to the constant term -222 may seem challenging to many students. Suggestion, to consider a cube closest to the constant term as (-216 -6 = -222 ) and associating -222 with a-cubed then factories from there. To sum up, in most cases, the constant term may lead you to early results. Another thing is that your solution in the form: X = log 6 / log 222 , is just good enough...........thanks.
@herbertwandha6110
@herbertwandha6110 13 күн бұрын
CORRECTION: Associating -216 with a - cubed.
@DommarajuJyothi
@DommarajuJyothi 13 күн бұрын
Ok
@herbertwandha6110
@herbertwandha6110 13 күн бұрын
In other words, the step : log(37) is not equal to log(36+1).Even log 4 does not mean log (2+2),but could mean log(2*2)=log2 +log2 Remember, you are on the world stage !.....blessings!
@DommarajuJyothi
@DommarajuJyothi 13 күн бұрын
I apologize for the error. I'll make sure to double check my equations in the future
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 16 күн бұрын
Good work🎉
@DommarajuJyothi
@DommarajuJyothi 16 күн бұрын
Thank you! 😊
@user-gd6ck8cr2p
@user-gd6ck8cr2p 17 күн бұрын
You' re great, please have a look at this: lnx^(cube root) +lnx=10.
@DommarajuJyothi
@DommarajuJyothi 16 күн бұрын
log x^(cube root) = log x^(1/3) = 1/3 log x 1/3 log x + log x = 10 ( base 10) 4/3 log x = 10 ( base 10) log x = 10 × 3/4 =15/2 ( base 10) log (base 10) of b = a then 10^ a = b. [ exponential logarithm formula) Therefore x = 10 ^ 15/2 x = 10^ 7.5 = 10^ ( 7+ 0.5) x = 10^7 ×10^ 1/2 x = 10^7 × 3.16227766 x = 31622.7766
@user-gd6ck8cr2p
@user-gd6ck8cr2p 16 күн бұрын
@@DommarajuJyothi very sorry, my fault, if f(x)=lnx, then f(x)^cube root +f(x)=10. {cube root √lnx +lnx=10, x=? , I know only the answer e to the 8}
@DommarajuJyothi
@DommarajuJyothi 16 күн бұрын
( log x)^1/3 + logx = 10 Let a = log x a^ 1/3 + a = 10 a = 8 log x = 8 x = e^8
@user-gd6ck8cr2p
@user-gd6ck8cr2p 16 күн бұрын
@@DommarajuJyothi 👍👍, EXCELLENT, may I ask you, which country are you from?
@DommarajuJyothi
@DommarajuJyothi 15 күн бұрын
I am from India 🇮🇳
@user-qy8re3yx3d
@user-qy8re3yx3d 17 күн бұрын
Очевидно, что а=5.
@libardouribe7617
@libardouribe7617 18 күн бұрын
👍
@ranaur1
@ranaur1 23 күн бұрын
You can also solve it using group theory properties. a^b mod c will always generate a cyclic group of order less than or equal to c. Also a^b mod c = (a^(b-1) mod c).a mod c. So its easier to calculate 5555*4mod 7 than 5555^2 mod 7. So, let' find the sequence 5555 mod 7 = 4 5555^2 mod 7 = 5555*4 mod 7 = 2. 5555^3 = 1. The cyclic group is (4,2,1) of order 3. 2222 mod 3= 2, so 5555^2222 mod 7 is the second element os the group = 2. Using the same reasoning 2222^5555 mod 7 has a group of order 5 and the 5 th element is 5. 2+5 mod 7 is, of course 0.
@DommarajuJyothi
@DommarajuJyothi 22 күн бұрын
Absolutely right! Great job spotting that
@UKPEINDANIELU.
@UKPEINDANIELU. 24 күн бұрын
Nice logarithm
@DommarajuJyothi
@DommarajuJyothi 24 күн бұрын
Thanks for the feedback! Logarithms can be tricky but they're also really interesting .Do you have a favorite math concept or topic you'd like to see covered next?
@DommarajuJyothi
@DommarajuJyothi 24 күн бұрын
Could you please subscribe my channel.
@UKPEINDANIELU.
@UKPEINDANIELU. 24 күн бұрын
@@DommarajuJyothi l need such logarithm questions
@DommarajuJyothi
@DommarajuJyothi 24 күн бұрын
Today's post is just what you needed! I posted another logarithm question, check it out and let me know what you think
@user-gd6ck8cr2p
@user-gd6ck8cr2p 18 күн бұрын
Can you solve please: (49 to the logx) +7=8.(x to the log7)?
@BaskaranRamachandran-fw1ce
@BaskaranRamachandran-fw1ce 25 күн бұрын
log(a+b) is not equal to log a+log b
@DommarajuJyothi
@DommarajuJyothi 25 күн бұрын
"Hi sir! Thank you for pointing out the mistake. You are absolutely right, the equation log(a + b) = log(a) + log(b) is not correct in general. I apologize for the error. The correct rule is log(a × b) = log(a) + log(b), known as the product rule of logarithms. I'll make sure to double-check my equations in the future. Thank you for helping me improve my accuracy!" Please subscribe my channel. Next time I will not disappoint you sir.
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 Ай бұрын
Good Job
@forgottenfamily
@forgottenfamily Ай бұрын
Before watching the video... A(n) = sum (x=0 -> n-1)(x*x!) 100! ? A(100) BUT n! = n*n-1! = (1 + n-1)*(n-1)! = (n-1)! + (n-1)*(n-1)! subtract (n-1)*(n-1)! from both sides n-1! ? sum(x = 0 -> n-2)(x*x!) = A(n-1) We can repeat this until we get to an easily calculable case 2! ? A(2): 2! ? 1*1 2! > 1*1 Therefore 3! > A(3) and so on until we get to 100! > A(100) (Watch) Well, that's a more precise solution
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you for sharing a more formal and precise proof using mathematical induction! Your approach is absolutely correct and provides a stronger foundation for the conclusion. By the recursively applying the formula and simplifying, you've elegantly shown that n!>A(n) for all n, including the specific case of 100! > A(100). Your input is invaluable. I appreciate the time you took to share your insight. This will certainly help others understand the problem more deeply. I hope you like the another concept that cubing of unique pairs 11^3, 22^3,... .If you like this content please subscribe my channel and we'll learn together.
@prach2
@prach2 Ай бұрын
X=1 ... by guessing.
@TECH-fk8to
@TECH-fk8to Ай бұрын
👍
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 Ай бұрын
Great Job 👍
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thanks! 👍
@TECH-fk8to
@TECH-fk8to Ай бұрын
👍
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you
@TECH-fk8to
@TECH-fk8to Ай бұрын
👍
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 Ай бұрын
Great job
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you
@Roham_planet__explains
@Roham_planet__explains Ай бұрын
Hello
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Hi, how are you
@TECH-fk8to
@TECH-fk8to Ай бұрын
Nice
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thanks
@TECH-fk8to
@TECH-fk8to Ай бұрын
👍
@unflexian
@unflexian Ай бұрын
thumbnail doesnt say its integer equation :(
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thankyou for your observation! While I didn't explicitly mention in the thumbnail that a &b are integers, I made sure to explain it during the video to ensure clarity for everyone. I appreciate your attention to detail and hope you found the explanation helpful!
@unflexian
@unflexian Ай бұрын
@@DommarajuJyothi yeah i saw, great videos from you ! keep up as long as you enjoy it:)
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thank you.
@anachronicity
@anachronicity Ай бұрын
Nice
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
" Glad you liked it!" Thanks for the encouragement
@pritamroy9320
@pritamroy9320 2 ай бұрын
That's a nice solution. Rigours from top to bottom. Only one input I'll give is that from the line (1+2a)(1+2b) = 17, it is more general to say that (1+2a) = either (1 or 17 ) or (-1 or -17) and consequently (1+2b) = either (17 or 1) or (-17 or -1 ). Since we are adding (1+2a) and (1+2b) to find (a+b) , it doesn't matter which one of them is 1 or 17 OR -1 or -17, the sum will be either 18 or -18. So in the end everything checks out.
@DommarajuJyothi
@DommarajuJyothi 2 ай бұрын
Thank you for your insightful input! I appreciate your suggestion for considering the general solutions of (1 + 2a) and (1 + 2b).
@legend_legend_legend
@legend_legend_legend 2 ай бұрын
or just set a = 0, so a+2ab+b = 0+0+b = 8 b=8 a =0 0+8 = 8
@DommarajuJyothi
@DommarajuJyothi Ай бұрын
Thanks for sharing your approach! While setting a=0 simplifies the equation, it's important to note that it only works for specific cases. Exploring various scenarios,like negative integers, allows for a more comprehensive understanding of the problem. Both methods have their merits in different contexts.
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 2 ай бұрын
Good work
@DommarajuJyothi
@DommarajuJyothi 2 ай бұрын
Thanks
@TECH-fk8to
@TECH-fk8to 2 ай бұрын
👍
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 2 ай бұрын
Keep going, great work
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 2 ай бұрын
Great work, proud of you.
@DommarajuJyothi
@DommarajuJyothi 2 ай бұрын
Thank you so much 😀
@TECH-fk8to
@TECH-fk8to 2 ай бұрын
👍
@TECH-fk8to
@TECH-fk8to 2 ай бұрын
👍
@TECH-fk8to
@TECH-fk8to 2 ай бұрын
Nice
@DommarajuJyothi
@DommarajuJyothi 2 ай бұрын
Thanks
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 2 ай бұрын
Great work
@DommarajuJyothi
@DommarajuJyothi 2 ай бұрын
Thanks
@charlesokuom8747
@charlesokuom8747 3 ай бұрын
Well explained
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
Thank you sir
@TECH-fk8to
@TECH-fk8to 3 ай бұрын
👍
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 3 ай бұрын
Nice👍
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
Thank you
@TECH-fk8to
@TECH-fk8to 3 ай бұрын
Nice explanation.
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
Thank you. Please subscribe to my channel
@TECH-fk8to
@TECH-fk8to 3 ай бұрын
Ok mam
@TECH-fk8to
@TECH-fk8to 3 ай бұрын
Good explanation.
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
😊
@TECH-fk8to
@TECH-fk8to 3 ай бұрын
Nice explanation.
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
Thank you.
@Xyz-fu4ns
@Xyz-fu4ns 3 ай бұрын
Nice
@DommarajuJyothi
@DommarajuJyothi 3 ай бұрын
Thank you
@raulrosu
@raulrosu 4 ай бұрын
Nice explanation and clean handwriting!
@DommarajuJyothi
@DommarajuJyothi 4 ай бұрын
Thank you, I really appreciate you taking time for me to express that. And please subscribe.
@TECH-fk8to
@TECH-fk8to 5 ай бұрын
👍
@anithaprakash8144
@anithaprakash8144 6 ай бұрын
Wow! Finding cube roots of decimal numbers had never been this easy before. Thank you for letting us know this trick. Kids will now enjoy and solve cube root related problems with much ease.
@DommarajuJyothi
@DommarajuJyothi 6 ай бұрын
Thank you so much for your kind words! I'm glad you found the video helpful. If you have any more questions , feel free to let me know. Your feedback means a lot!" 🙏
@TECH-fk8to
@TECH-fk8to 6 ай бұрын
👍
@nehithasrim.g.6070
@nehithasrim.g.6070 7 ай бұрын
Supper akka
@DommarajuJyothi
@DommarajuJyothi 7 ай бұрын
Thank you
@sudhakarpadmaraju7592
@sudhakarpadmaraju7592 7 ай бұрын
Great tip!
@DommarajuJyothi
@DommarajuJyothi 7 ай бұрын
Thank you
@philipwaters5043
@philipwaters5043 7 ай бұрын
Great tips! What do you do if your number ends in a 2 or 3?
@DommarajuJyothi
@DommarajuJyothi 7 ай бұрын
Thankyou for your insightful question about square roots! I appreciate your curiosity. If you have any more math queries, feel free to ask. As for the answer, square numbers end with 0,1,4,5,6 or 9. If a number ends with 2,3,7 or 8 that number is Non-perfect square number. " In my upcoming video, I'll be explaining perfect and Non-perfect square roots.
@PremKumar-fl6kf
@PremKumar-fl6kf 7 ай бұрын
Very informative👍🏼
@DommarajuJyothi
@DommarajuJyothi 7 ай бұрын
Thank you