14 күн бұрын
7 ай бұрын
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@Usha-gh4sx 8 күн бұрын
Om shree guru raghavendra namah 🙏🙏🙏🙏🙏
@AmmeMahamaye 15 күн бұрын
🙏🏾🙏🏾🙏🏾🙏🏾Mahalaxmi Mataji🙏🏾
@SenthilKumar-k7j 19 күн бұрын
🙏🙏🙏🙏
@aimsdaretosuccess 8 ай бұрын
Iam 108th subscriber
@NumberPen 8 ай бұрын
thanks much. i am glad to hear that. i have subscribed to your channel as well. hope u see more and more success.
@mdasifeqbal2323 9 ай бұрын
Please can you consider this question for a video. If f(t) = sint, g(t) = cost. Find the value of: Limit 0 to π/2, [{f(2x)}^2 + {g(2x)}^2]dx
@NumberPen 9 ай бұрын
Hi Asif. thanks. are u referring to definite integral of the function above.
@mdasifeqbal2323 9 ай бұрын
@@NumberPen Yes. This question just came to my mind and I wrote it down. Though the question is based on the fundamental concepts but can be asked as an objective question.
@mdasifeqbal2323 9 ай бұрын
If f(2t) = sin2t, g(2t) = cos2t. Find the value of: Limit 0 to π/2, ∫ [{f(3x)+ g(3x)}^2 + {f(3x) - g(3x)}^2]dx
@NumberPen 9 ай бұрын
@@mdasifeqbal2323 I will definitely address it when I come to definite integrals. thanks much.
@mdasifeqbal2323 9 ай бұрын
@@NumberPen Thanks for considering the questions.
@HappyCatfish-ie2fs 9 ай бұрын
Thank you so much 🙏
@NumberPen 9 ай бұрын
You're welcome 😊. Hope you liked my presentation and discussion in this video.
@mdasifeqbal2323 10 ай бұрын
Perfect and time-saver method.
@mdasifeqbal2323 10 ай бұрын
Why don't you use 2cosAcosB formula? You have solved this problem in a very complex and lengthy method.
@NumberPen 10 ай бұрын
Yes Asif. I would have mentioned that during the video. I just wanted to attempt using basic trig identities we know. Students will also have to learn how we approach these problems right. U notice that ultimately I land at the same output what u otherwise get by applying the sum product formula.
@NumberPen 10 ай бұрын
Imagine if someone did not know the identity or does not remember it
@mdasifeqbal2323 10 ай бұрын
@@NumberPen You reached at the same step as I mentioned but it took time to complete some more steps. I have 20+ years of experience in teaching Class 11 & 12 mathematics, and I as per my experience, it's best to tell the best method to the students. Later, they can try their own lengthy method on their own. If the best and short-cut method is provided then it will be very easy for them to attend all the questions and secure very good marks in the examinations.
@mdasifeqbal2323 10 ай бұрын
@@NumberPen For this, I always take tests on formulae. Also, I take tests on chapters.
@NumberPen 10 ай бұрын
@@mdasifeqbal2323 Hi Asif - Good day I have also solved the problem using sum product formula here kzbin.info/www/bejne/lZimeoaGjaiooKs . Thanks for your feedback and suggestion.
@mdasifeqbal2323 10 ай бұрын
Keep x on right side and make sin(a+y) as denominator on the other side and then differentiate wrt y and you will get dx/dy and sin^2(a+y) in the denominator on the other side, and then reverse it to make it dy/dx and you will get the answer. This is the shortest method.
@NumberPen 10 ай бұрын
Yes. That is another way. Cool. Thanks.
@mdasifeqbal2323 10 ай бұрын
Magic method.
@NumberPen 10 ай бұрын
Many many thanks. Hope u liked it
@mdasifeqbal2323 10 ай бұрын
@@NumberPen Yes
@Qoe8playz 11 ай бұрын
I understand it for forever 🎉🎉
@NumberPen 11 ай бұрын
thank you, hope you liked it. please feel free to pass me any constructive feedback as well.
@ErnestoGARCIA-gz8hc 11 ай бұрын
Muy buen limite, excelente aporte, muchas gracias mis saludos desde la victoria, Aragua, vebezuela
@NumberPen 11 ай бұрын
Thanks, yes. this is an interesting problem . Hope you liked it.
@ErnestoGARCIA-gz8hc 11 ай бұрын
Thanks por valioso aporte , saludo desde La victoria , Aragua, venezuela
@NumberPen 11 ай бұрын
thank you . gracias !!!
@bhupendrajaybharat Жыл бұрын
Very ni○e efforts
@NumberPen Жыл бұрын
thank you bhupendra ji