Bprp, I really want to show you how I had come across that 0/0=0. I have a very in depth set of ideas that I would love to be able to show pertaining to infinity, 0+, 0-, and ÷0. There is also a part about how i is similar in cases and what my opinions are on 0^0. I am 17 years old and love math, and I would love to share what I have calculated in my free time. This work is all mine and I have not seen anything like it on the internet or RUclips. If you do put some of my work in a video for division by 0, please reference me or ask me about it!
I wish I could remember my Calc III final (from about 1989). There was a question worth about a zillion marks: "Prove such and such." I was about half-way through when I realized I was going in the wrong direction, so I started over. Eventually I got stuck. Now I had two solutions in the form of equations. I substituted one into the other, turned the crank, and got 0. That couldn't be an accident, so I wrote QED and went to the next question. I ended up with a decent grade in the course. I never got the review the graded exam, but I must have done something right.
I took my BC test during the 3rd administration, and boy, the last FRQ was actually pain. I think I just had 8 minutes for this problem alone because it was so hard to type and explain my work, not to mention the question was pretty difficult as well. Pretty much everyone in my class hated the 2 BC FRQs, while AB ones were a walk in the park.
@@wingedshell3518 My plan is to skip the formal class because I know enough that I would be bored for a significant portion of the year. As a last resort I'll take it, but the plan is to add a bit more structure to my study with either regular online courses or individually paced (but curriculum-aligned) online courses, and take the exam in May.
On part b when you said you wanted the ratio to be greater than 0, I think you just meant it needed to be a finite number. Since you put a known convergent series in the denominator, you could actually have gotten zero for the ratio and the series in the numerator would still converge. You really don’t need to worry about it being positive since you took absolute value at the beginning (and it was already known that 1/e^n was positive). On the two infinite limits, I don’t think AP minds if you use ‘dominating terms’ or similar reasoning to get to the answer instead of going through L’Hospital’s Rule. This was a fun problem! I also like how you took 14 minutes to record it, almost perfect pace. :)
I’m so glad I didn’t get this version of the calc bc test-this section would of absolutely demolished me (it was funny however because during the entire test I forgot everything about series until I got to question 6 of the frq, and it all clicked, so that was great)
At 6:00 a way we saw at our school to solve such fractions is to factor out the term that grows the most (here e^n). You would then get lim n->\inf \frac{e^n}{e^n(2+3/e^n)}. Then, both e^n cancel each other and you're left with \frac{1}{2+3*e^-n}, which converges to 1/2. This seems to be a somewhat formal way to explain the fact that the 3 doesn't matter
Yes, you can do that, though it doesn’t simplify all problems. Since this is a series problem, you would have already learned L’Hospital’s rule, so I would just use that or just do it the way BPRP does it.
regarding b): first off, you dont even need the limit comparison test. it is obvious that 2e^n+3 > e^n for all n, which means (e^n+3)^-1 < (e^n)^-1 for all n, which immediately implies that the series converges. secondly, why cant you use the LCT if the limit is 0? if lim a_n/b_n = 0, that means that a_n
Can you do a video on linear, algebra, matrixes, vectors, gradients, and partial derivatives and applications of these mathematical concepts in the real world?
Hey BPRP, your videos are always so useful and entertaining. I do want to ask one question. Whats the difference between a maclaurin series and a taylor series. My math paper gives us maclaurin series for e^x sinx cosx and ln(1+x), but they are the same as the taylor series that I saw in your videos. Are they the same with just a different name, or is there some difference?
@@krishnannarayanan8819 ok so near the end, I ended up getting my crap together and I actually started doing really well. I thought the exam was easy and got a 5, but no, I got a 3 and an ab ab score of 4.
For part b, you could just do a normal comparison test with 1/(2e^n), and since this converges, we get that the desired summation also converges (it is always smaller) Edit: I realized that the question asked to use LCT, oops.
@blackpenredpen - I want to buy your t-shirts "Derivatives For You" and "Integrals For You", but your 'Spring' website-to-purchase link returns an error today (May 2) :-( -- please advise, thank you in advance. BTW, *your math lectures are excellent, thank you!*
Yeah no offense, but I don't think your radius of convergence formula would've flown on the actual exam. They probably would've wanted you to use the ratio test, annoyingly. Still works though
This is the AP Calc test I took when I was in HS: ruclips.net/video/DHDC3oOy178/видео.html
Sir I proof Riemann hypothesis is NP complete problem.
Sir you know 1 million dollars P vs NP problem
Bprp, I really want to show you how I had come across that 0/0=0. I have a very in depth set of ideas that I would love to be able to show pertaining to infinity, 0+, 0-, and ÷0. There is also a part about how i is similar in cases and what my opinions are on 0^0. I am 17 years old and love math, and I would love to share what I have calculated in my free time. This work is all mine and I have not seen anything like it on the internet or RUclips. If you do put some of my work in a video for division by 0, please reference me or ask me about it!
I wish I could remember my Calc III final (from about 1989). There was a question worth about a zillion marks: "Prove such and such." I was about half-way through when I realized I was going in the wrong direction, so I started over. Eventually I got stuck. Now I had two solutions in the form of equations. I substituted one into the other, turned the crank, and got 0. That couldn't be an accident, so I wrote QED and went to the next question.
I ended up with a decent grade in the course. I never got the review the graded exam, but I must have done something right.
I took my BC test during the 3rd administration, and boy, the last FRQ was actually pain. I think I just had 8 minutes for this problem alone because it was so hard to type and explain my work, not to mention the question was pretty difficult as well. Pretty much everyone in my class hated the 2 BC FRQs, while AB ones were a walk in the park.
Just saw this, and remembered i just took the 2018 as a practice gauge for my self study a week or two ago! Yay for more FRQ practice :)
Most of it actually came from these videos; they helped me keep going forward with it!
That’s cool! Are you going to take the class? Or doing it just for fun, or taking calculus in college
@@wingedshell3518 My plan is to skip the formal class because I know enough that I would be bored for a significant portion of the year. As a last resort I'll take it, but the plan is to add a bit more structure to my study with either regular online courses or individually paced (but curriculum-aligned) online courses, and take the exam in May.
@@Sean-of9rs that sounds really cool, I’m happy that you have things planned out for you! I wish you the best of luck!!
@@wingedshell3518 Thanks! Whatever you're doing, I wish you the best of luck as well. It's never too early or late to learn something.
On part b when you said you wanted the ratio to be greater than 0, I think you just meant it needed to be a finite number. Since you put a known convergent series in the denominator, you could actually have gotten zero for the ratio and the series in the numerator would still converge. You really don’t need to worry about it being positive since you took absolute value at the beginning (and it was already known that 1/e^n was positive).
On the two infinite limits, I don’t think AP minds if you use ‘dominating terms’ or similar reasoning to get to the answer instead of going through L’Hospital’s Rule.
This was a fun problem! I also like how you took 14 minutes to record it, almost perfect pace. :)
Good catch as errors here are very rare.
I love when the questions are harder than expected but give you some hints and steps
I’m so glad I didn’t get this version of the calc bc test-this section would of absolutely demolished me (it was funny however because during the entire test I forgot everything about series until I got to question 6 of the frq, and it all clicked, so that was great)
Dude same, definitely would not have done well on this question. Whatever I got on my exam seemed way more strait forward.
At 6:00 a way we saw at our school to solve such fractions is to factor out the term that grows the most (here e^n). You would then get lim n->\inf \frac{e^n}{e^n(2+3/e^n)}. Then, both e^n cancel each other and you're left with \frac{1}{2+3*e^-n}, which converges to 1/2. This seems to be a somewhat formal way to explain the fact that the 3 doesn't matter
Yes, you can do that, though it doesn’t simplify all problems. Since this is a series problem, you would have already learned L’Hospital’s rule, so I would just use that or just do it the way BPRP does it.
6:03 we can use comparison test else
Took AP Calc last year and it seems I’ve forgotten everything this video covers :/
Ours was also way easier tbh
I really like math and enjoy these videos
I love your new profile picture. To me the pens looks like Nintedo Switch controlls.
Thanks
And 😆
@@blackpenredpen same for me!!!! You are awesome 😎😎😎 wish you 1 million subscribers soon! I love your new profile picture 🤩🤩🤩🤩
regarding b):
first off, you dont even need the limit comparison test. it is obvious that 2e^n+3 > e^n for all n, which means (e^n+3)^-1 < (e^n)^-1 for all n, which immediately implies that the series converges.
secondly, why cant you use the LCT if the limit is 0? if lim a_n/b_n = 0, that means that a_n
I DID THIS THANK YOU SO MUCH!!!!!
For question b you can also use the alternating series because each terms is the opposite of the next one and the sequence goes to 0.
I'm shuddering, BPRP you showed me my worst nightmare
Can you do a video on linear, algebra, matrixes, vectors, gradients, and partial derivatives and applications of these mathematical concepts in the real world?
Great job as usual! Keep up the good work
Sir Can you make a video on Geometrical proof of tan ( a + b ) ?
Yes, I would like that too!
Omg, I don't like questions with so many multiple parts😅 great video!
😆 thanks!
This is all right. Thank you so much 😇
Divide the numerator and the denominator by the biggest infinity in the denominator to solve those limits properly.
Hey BPRP, your videos are always so useful and entertaining. I do want to ask one question. Whats the difference between a maclaurin series and a taylor series. My math paper gives us maclaurin series for e^x sinx cosx and ln(1+x), but they are the same as the taylor series that I saw in your videos. Are they the same with just a different name, or is there some difference?
iirc Maclaurin series are just Taylor series centered at c=0
Ok thank you bery much. It has been causing me a lot of confusion.
Amazing video as always ^^ well done 👏👏
No I did not get the question right
I love your videos so much. They are very helpful. Could you make some videos about Hermite ODE and Hermite polynomials?
Sir I proof Riemann hypothesis is NP complete problem.
Sir you know 1 million dollars P vs NP problem
Very Interesting Problem
Try to solve the reimann hypothesis
I solved it already.
Yeah I just skipped over the whole frq… definitely gonna need to retake it in college
I’m about to get a 1 on this BC exam in May.
How did it go?
@@krishnannarayanan8819 ok so near the end, I ended up getting my crap together and I actually started doing really well. I thought the exam was easy and got a 5, but no, I got a 3 and an ab ab score of 4.
For part b, you could just do a normal comparison test with 1/(2e^n), and since this converges, we get that the desired summation also converges (it is always smaller)
Edit: I realized that the question asked to use LCT, oops.
Hello Steve and everybody!
Very nicely done ☺️✅✅✅ I feel so relaxed
Dr weselcouch would be jealous if he saw this 😂 jk
@@tzonic8655 y?
Please can you do some STEP 3 questions. I can see you have done a STEP 2 but STEP 3 is much harder. Thank you
Here’s a question, does x/(x/(x/(x…) = sqrt(x)?
Amazing video
If x+y=5
How much is the amount of
x3+15xy+y3
Numbers are an illusion, its just black pen and red pen
Hard integrals are not a thing, it is just blackpenredpenbluepenpurplepen
@blackpenredpen - I want to buy your t-shirts "Derivatives For You" and "Integrals For You", but your 'Spring' website-to-purchase link returns an error today (May 2) :-( -- please advise, thank you in advance. BTW, *your math lectures are excellent, thank you!*
I am just a grade 12 student in India and I am able to understand these stuff. I wish I already knew these concepts...
Prove: For all x ϵ R (set of real numbers), f(x) = 2x + 3 is a one-to-one and onto function
Really informative, excellent content!
We're taught integeral calculus today.... it's pretty hard for me. How can perform in an effective manner?
please solce root 2 ^ root 2
Confucious of Math, greetings!
Can you please tell how to find 0.6^√3
First 5 seconds in and first thought is man's beard is majestic
isnt this a question from the second administration of the test
Doubt: ∫ √(x/x-1)dx
Thank you 😀
Hello everyone and Steve
Hey Sergio!! Hope all is well!
i like you so much!!!!!!!!!! VERY FUN PROBLEM! YOU SE THE CHEN LU!!
5:54 bro just factor top and bottom by e^n ...
Is there any way to calculate the function g(x)?
The part a Can be solve by saying it's a geometric series
Question asks only for integral test though
Yeah no offense, but I don't think your radius of convergence formula would've flown on the actual exam. They probably would've wanted you to use the ratio test, annoyingly. Still works though
He did use the ratio test, just a shortcut formula version of the way it’s normally presented in textbooks. I think it’s fine.
Unfortunately, I can’t check. I got a different question 6.
Taking AP calc bc next year and this is not making me feel better lol.
Hmm
How do you do (2i)^i ?
There logo is changing monthly
Hello! I'm a teacher of AP Calc. Just wanted to ask if that whiteboard you're using is mounted on a portable / movable stand? Thanks! Kalpit, India
What is your name Sir?? Please , I want to know,,,,,
The title looks juicy …
Fun Fact: 1+2+3+4+5.......= -1/12
No it doesn't, it diverges
@@obinnanwakwue5735 it does search it up for proof
@@abd_sh_321 searched it up, it doesn't. The Riemann zeta function does assign the series a value of -1/12 but it doesn't equal such.
@@obinnanwakwue5735 So you think that I would seriously Write a non-manipulative, and non-clickbaity fun fact
No, I don’t think I did.
i dont remember doign this
Solve 1/0 😎
🥇 first
"As b goes to n-fiin-it-ee." :)