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you're a celebrity in my math class. we all talk about you, because we've all watched you. i was doing a problem on the board and my professor asked me if i watched "the organic chemistry turor" because she noticed that my notation was almost identical to yours. thanks man. i really appreciate your work
You just saved me! My calc 2 class went online and my textbook is extremely bare-bones and my teacher doesn't know how to do video lectures. Thank you so much for being so in-depth!
I don't know if its the way you articulate each step over and over, even the smallest things, but I have studied your videos for a few hours and feel like I have genuinely studied this stuff for months. Its the way you set up your videos and subtly introduce nuances and slight difficulties so that when Im done I realize I have done all the problems with "tricks" and see how the concepts relate to each other. Truly brilliant.
come on people just like two or three more sections to go then calc 2 is over we can do this!!! This is the hardest class i have taken so far without a doubt but it will all be over soon.
I've been stressing over this stuff for the last 48 hours. My textbook and our math resource room was unable to help. You came to my rescue. I thank you sir!
Can we all just appreciate this man and his ability to save me on every single one of my calc tests. Explanations more clear than my actual Calc Professor
@@mintberry6014 Same here, I am retaking it even if I end up with an "A". I need 88.5 on final to get an A which looks too big of a goal but I am on right track watching this awesome tutor...
Honestly dude, thank you so much. Your videos literally help with anything. Some lectures just buzz through and don't truly get into need-to-know details. You make everything so simple and understandable.
I have an exam on this tommorrow and you didn't have these videos out at the beginning of the unit but you made them just in time!! Literally watching his videos makes everything so much easier to understand!!!!
I have a fighting chance at my exam in a few hours because of your videos. Thank you SO MUCH for making these and for going over multiple examples of each type of problem in each vid. You're the best!! 😍
I have been using your videos since I was doing IGCSE O-level Cambridge examinations and now look at me in college still using your videos. I understand calculus 2 because of you! I know I'll be back on your youtube channel for calculus 3. You're my mathematical hero!! God Bless you * infinity!!
This is such a blessing during COVID-19 times, especially since classes have been suspended. I can barely understand during class, and this is beyond helpful!! Thank you so much for your hard work and now I can pass my final tomorrow.
Very thorough, articulate and clear. Fantastic job. The future of affordable learning as tuition is becoming an obstacle to education, we need more bright and generous souls like yours to make it happen. I look forward to the day when education becomes an open source project with tailored curriculum to fit any need. We need to abandon the politics of degrees and replace it with deep understanding of the subjects required to perform certain tasks. This is not undermining the value of formal education with all its elective requirements, mainly humanities and liberal arts subjects, but when cost of education becomes a problem, we need to prioritize our needs. Thanks a ton!
You are amazing ! Got my exam in couple of days and i'm really confident about it because of your videos! The stuffs my profs teach in couple 3-4 hours you teach it in less than an hour.
Professor Organic Chemistry Tutor, thank you for an awesome introduction and analysis of the Power Series Representation of Functions in Calculus Two. Power Series Representation of Functions has played an important role in the development of Calculus. Once you define a function with a Power Series, it is also important to analyze the characteristics of the function. Continuity, Differentiability and integral ability are important characteristics of a function in Calculus. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
your content is a godsent help, everytime I see you on something i search I know I'm gonna fully understand it, I wish you had time stamps though but thats a small nit-pick from the brilliant content you post
Clarification Question: at about 43:30 you say that r is -x/2. does the x^3 in the numerator of the original function not impact what r is? is r the same for both x^3/x+2 and 1/x+2?
im not 100% sure but I think there is a mistake 20:00, when u factor 1/3 from the denomnator that should result in a 3/(1 - (x/3)) which the should turn into 3(x/3)^n which is x^n / 3^(n -1)
Notice that he’s not factoring he’s multiplying by 1/3 on top and bottom u can also do factoring on the bottom which touching the top tho I like it this way too
3 is the same as 2 + 1 so 1/3-x is the same as 1/2+1-x and since we want to represent the fn. in the form of 1/1-r so we will move the 2 next to the x so the fn. will be 1/1-x+2 now a = 1 and r = (-x+2)
@@mohanadnada4670 Ahmet clearly knows this (they have already broken it down to the same step you got to). Also, you forgot to factor out a -1 between your last 2 lines, so your r is off. The question is why does Ahmet get such a different looking power series by choosing r = (x-2), a = 1 than the video did. The long and short of it is that the two series, while looking very different, both will give the same results where there is convergence. By choosing r = (x-2), the series is centered at 2 with radius 1, so it only converges between 1 and 3. However, the solution provided in the video has a larger radius of convergence, spanning between -3 and 3. Therefore, the two different ways of writing the power series are not in fact the same; they only have equivalent infinite sums for x values between 1 and 3. You can verify this non-rigorously by plugging in a couple values of x within the radius of convergence for both series. They should be pretty close depending on how many terms you calculate out to.
Miklos Obrusanszki This is equivalent to multiplying each term in the series by x^3 by distribution. So by bringing the x^3 inside the summation, you’re also multiplying each term by x^3 directly without distributing.
I have a question arund the minute 18:19, it is ok when we do the root cube of the value (-1) < X < 1, it is still possible to say that is (-1), isnt it an imaginary number, i may be wrong. just a bit confused.
if you were confused like I was (maybe I'm just stupid) . @ 5:04 r (lowercase) is the rate of the geometric sequence, and R (capital) is the radius of convergence.
At 28:40: Why could you not first simplify by dividing through by 2? Then you'd have 4/(x-(9/2)) which completely changes the answer. Why does this not work?
Why do the two identical problems, one starting at 18:26 and one at 21:37 , start out identically but solve to difference radius s and different intervals???? They start out identical and you provide steps to reach 2 completely different answers???
done thanks! I realized that you can add constants to make denominator into 1-x but it kind of changes the overall power series function, that's why I think *the unwritten rule when transforming a function into a power series function is that when transforming them into a/1-r you should not change the overall value of the function*, therefore it's preferred to just multiply or divide num/den but when adding a constant, make sure it is =0, just like 1-1 =0, because adding a higher value to make dennominator 1-x introduces a new constant and changes the resulting power series. I got a different answer on my side.
The formula is a / 1 - r; the negative in the " 1 - r " is part of it, so you would not include it. However, if it was, for example, a / 1- ( -r ) , you would include it as such.
What if the function you're given is xln(1+x) and the center is at 2? Sorry if this is a dumb question, this is during the COVID-19 quarantine and my calc professor gave up on us. No lectures, just homework that doesn't explain anything.
2 * 2^n = 2^(n+1) not 4^(n+1) hope that makes sense. For example try plugging a number into "n" and see what you get. You should understand if you do that :)
Hi teacher, may I ask about one of the examples? 1/(3-x) can also be changed to 1/(1-(x-2)), so a=1, r=x-2 But finally my answer is not the same as yours. The radius of convergence i found is 1, interval of convergence is (1,3). Am I missing any concepts ?
I have a function f(x)=1/(2-x) and i rewrite it as f(x)=1/(1-(x-1) which gives us a=1 and r=(x-1). However in my textbook it says that a=1/2 and r=(x/2)?
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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pretty suspicious you comment this the exact day i need these vids man
You and khan relly allow me to study ahead
behind every successful student stands the organic Chemistry Tutor
you're a celebrity in my math class. we all talk about you, because we've all watched you. i was doing a problem on the board and my professor asked me if i watched "the organic chemistry turor" because she noticed that my notation was almost identical to yours. thanks man. i really appreciate your work
does that mean ur prof watches too lol
@@JasonPwnsAll ahhahaha
We call him in our class "The Oct"
@@BlackZephyrReal we say "The O-Chem tutor".
I have a feeling theses videos are about to blow up from all the students trying to get help for their online classes because of COVID-19
Loraine Sperling here I am struggling to keep up wit my online class
@@mohamadelgendy4095 lolol
Isn't it wild we still pay full tuition? Smh
God bless the everything tutor!
can't agree more
You just saved me! My calc 2 class went online and my textbook is extremely bare-bones and my teacher doesn't know how to do video lectures. Thank you so much for being so in-depth!
I don't know if its the way you articulate each step over and over, even the smallest things, but I have studied your videos for a few hours and feel like I have genuinely studied this stuff for months. Its the way you set up your videos and subtly introduce nuances and slight difficulties so that when Im done I realize I have done all the problems with "tricks" and see how the concepts relate to each other. Truly brilliant.
this comment ^
come on people just like two or three more sections to go then calc 2 is over we can do this!!! This is the hardest class i have taken so far without a doubt but it will all be over soon.
AdvancedDynamicDisplacement Idk if you have or need to take calc based physic or not, but that’s gonna hit you like a train.
@@nwshiar Do not need to fortunately I have heard that is wild
Bless you for your comment. I am left with two weeks of school and believe me when I say your comment has given me so much encouragement!
@@tinochigwada4652 that exactly why i posted it my brother everyone who comes here needs motivation
try taking both together....
I've been stressing over this stuff for the last 48 hours. My textbook and our math resource room was unable to help. You came to my rescue. I thank you sir!
Thanks!
Can we all just appreciate this man and his ability to save me on every single one of my calc tests. Explanations more clear than my actual Calc Professor
watching 1 day before final exam
Welcome to the Calc 2 struggle bus 😂😂😂
that's no joke... I made the unfortunate decision to take it over the summer.....
As soon as you barely feel comfortable with something, you get thrown back into the deep end, confused and scared.
@@mintberry6014 Same here, I am retaking it even if I end up with an "A". I need 88.5 on final to get an A which looks too big of a goal but I am on right track watching this awesome tutor...
Shoutout to all the German university students where, for some bizarre reason, calc1-3 is combined into Analysis 1, lol
@Palpatine Welcome to mathematics, Senate. You are dealing in absolute.
Honestly dude, thank you so much. Your videos literally help with anything. Some lectures just buzz through and don't truly get into need-to-know details. You make everything so simple and understandable.
i'm taking my calc 2 final today and i've been on ur page ALL DAY, hope it pays off
Did it?
I think I've watched the majority of your videos. You are a master teacher over the web. Thank you so much for this and all other videos you do.
I have an exam on this tommorrow and you didn't have these videos out at the beginning of the unit but you made them just in time!! Literally watching his videos makes everything so much easier to understand!!!!
this man really knows how to do everything
I have a fighting chance at my exam in a few hours because of your videos. Thank you SO MUCH for making these and for going over multiple examples of each type of problem in each vid. You're the best!! 😍
3 years later, how'd ya do
Same
I have been using your videos since I was doing IGCSE O-level Cambridge examinations and now look at me in college still using your videos. I understand calculus 2 because of you! I know I'll be back on your youtube channel for calculus 3. You're my mathematical hero!! God Bless you * infinity!!
This is such a blessing during COVID-19 times, especially since classes have been suspended. I can barely understand during class, and this is beyond helpful!! Thank you so much for your hard work and now I can pass my final tomorrow.
Been watching this vid and slowly working along for the past 5 hours haha. Life of a math student. Thanks for these videos!
Teaching yourself math looking up good videos like this is better way to learn and you learn more than in class
Respect to you sir! 5 hours!
Very thorough, articulate and clear. Fantastic job. The future of affordable learning as tuition is becoming an obstacle to education, we need more bright and generous souls like yours to make it happen. I look forward to the day when education becomes an open source project with tailored curriculum to fit any need. We need to abandon the politics of degrees and replace it with deep understanding of the subjects required to perform certain tasks. This is not undermining the value of formal education with all its elective requirements, mainly humanities and liberal arts subjects, but when cost of education becomes a problem, we need to prioritize our needs. Thanks a ton!
You are amazing ! Got my exam in couple of days and i'm really confident about it because of your videos! The stuffs my profs teach in couple 3-4 hours you teach it in less than an hour.
God bless you, man 🙌🏼😭. you doing God’s work out here by helping us struggling students.
I can not explain how detailed and awesome u teach. U R a hero in my opinion
Thank you. Really thank you. You have saved my calculus grades and my career goals
I feel like no math book is perfectly complete in examples. This dude time and time again fills in those missing gaps.
Thank you so so much for this, these videos on Calc II are the only reason I'm understanding the material properly!!!
Woah you teach everything from math to chemistry
Damm
Thanks a lot
At 48:42, why it shows as 1/x+2 instead of -1/x+2 somehow?
it's brought back at the end of the video
Awesome work JG! Just when I thought I conquered all algebra, it took Calculus 2 to teach me more algebra =)
My god, thank you! Gotta love struggling in the hardest unit of the hardest calc class...
Professor Organic Chemistry Tutor, thank you for an awesome introduction and analysis of the Power Series Representation of Functions in Calculus Two. Power Series Representation of Functions has played an important role in the development of Calculus. Once you define a function with a Power Series, it is also important to analyze the characteristics of the function. Continuity, Differentiability and integral ability are important characteristics of a function in Calculus. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
your content is a godsent help, everytime I see you on something i search I know I'm gonna fully understand it, I wish you had time stamps though but thats a small nit-pick from the brilliant content you post
for the number at 21:27 , some one tell me why we dont use (1+2) as a replacement for three to make the function fit the GP template (a/(1-r))
because we need to ensure that C value is=0 following the problem's request
Clarification Question: at about 43:30 you say that r is -x/2. does the x^3 in the numerator of the original function not impact what r is? is r the same for both x^3/x+2 and 1/x+2?
Galatoomii baayyee gaaridha!!!!!!!!!!!!
Thanks!!!!!! very good!!!!!!
im not 100% sure but I think there is a mistake 20:00, when u factor 1/3 from the denomnator that should result in a 3/(1 - (x/3)) which the should turn into 3(x/3)^n which is x^n / 3^(n -1)
Notice that he’s not factoring he’s multiplying by 1/3 on top and bottom u can also do factoring on the bottom which touching the top tho I like it this way too
at 30:30 was the negative factored out wrong or am I missing something?
thats what i was thinking too
Not gonna lie, I watch all your videos on 1.25x speed
His speed is good for me
His speed is perfect
That's smart actually lol
I watch his videos on 2x speed, lolz.
For me it depends haha, if it is relatively easy I watch it in 2x but if it's challenging I watch it in 1.25x. His normal speed is too slow for me😂
Test on this in 2 hours… wish me luck
18:30 , why do we solve the problem by making 1 / (1-(x-2))? The answer becomes different than video's. Could you explain to me why it is different?
3 is the same as 2 + 1
so 1/3-x is the same as 1/2+1-x
and since we want to represent the fn. in the form of 1/1-r
so we will move the 2 next to the x so the fn. will be 1/1-x+2
now a = 1 and r = (-x+2)
@@mohanadnada4670 Ahmet clearly knows this (they have already broken it down to the same step you got to). Also, you forgot to factor out a -1 between your last 2 lines, so your r is off. The question is why does Ahmet get such a different looking power series by choosing r = (x-2), a = 1 than the video did. The long and short of it is that the two series, while looking very different, both will give the same results where there is convergence. By choosing r = (x-2), the series is centered at 2 with radius 1, so it only converges between 1 and 3. However, the solution provided in the video has a larger radius of convergence, spanning between -3 and 3. Therefore, the two different ways of writing the power series are not in fact the same; they only have equivalent infinite sums for x values between 1 and 3. You can verify this non-rigorously by plugging in a couple values of x within the radius of convergence for both series. They should be pretty close depending on how many terms you calculate out to.
@@michaelwhite1552 thanks man, it was really helpful.
I always can find best explanation for my math courses .
This is easily the hardest part of calc 2. Thank god I did good in the other chapters so my grade can afford it
At 43:09 why are we able to just multiply the x^3 into the summation?
Miklos Obrusanszki This is equivalent to multiplying each term in the series by x^3 by distribution. So by bringing the x^3 inside the summation, you’re also multiplying each term by x^3 directly without distributing.
I have a question arund the minute 18:19, it is ok when we do the root cube of the value (-1) < X < 1, it is still possible to say that is (-1), isnt it an imaginary number, i may be wrong. just a bit confused.
Man, you're a lifesaver
Also at 28:41, How do you come up with 3 as the center?
thats what you are trying to find. its like if hes asking the question: "find the power series representation of the function: 8/2x-9 centered at x=3"
Exactly what I needed & perfect timing for next week's exam!
Wow! What a wonderful lecture!
there is one thing to say about this video, 'LIFE SAVER.'
Excellent. I Feel like I'm ready for the mathematics olympiad
Ridiculously good video.
this video is way better than my professor's lecture!!!! saves me from my final
I'm so confused.... when c does not equal 0 at 22:07 you put it in the (x-1) term, but when c does not equal 0 at 29:46 it goes to the 1/1-x???
I hope nothing but good things happen for you sir
this man is carrying me thru college holy shit thank you so much
At 29:00 where did you get c=3?
From 2(x-3)
if you were confused like I was (maybe I'm just stupid) . @ 5:04 r (lowercase) is the rate of the geometric sequence, and R (capital) is the radius of convergence.
U saved me ❤ i survived god bless u ❤❤❤
Infact this man is a hero❤❤❤
thank you so much for these videos. you are helping so many students!!
Thanks a lot bro your explanation so helpful
at 49:30 isnt the 1/x+2 negative?
Yeah it is
Dude you are a life saver
omg thank you thank you sooo much my prof made it so confusing but 2 minute into the video I understood what's happening
you r a good man...
Thank you for the wonderful explanation as always but I have a question. What if the intervals are given for example -1
Are all power series representing a function have an open interval or do we have to test the endpoints in every problem?
At 28:40: Why could you not first simplify by dividing through by 2? Then you'd have 4/(x-(9/2)) which completely changes the answer. Why does this not work?
I know this is late but you would be changing the value of the equation.
Amazing, thank you! I hope you're well
My professor sucks so bad. You’re the only reason I’m going to pass calc 2 lol
Why do the two identical problems, one starting at 18:26 and one at 21:37 , start out identically but solve to difference radius s and different intervals???? They start out identical and you provide steps to reach 2 completely different answers???
he centered the first one at 0, the second one was centered at 1
this is all good material, but now how do you deal with functions like sin(x)? :)
do people use calculus in organic chemistry?
You saved my life
In the last example can not I just use completing square in the denominator and solve it as the previous examples ?
done thanks! I realized that you can add constants to make denominator into 1-x but it kind of changes the overall power series function, that's why I think *the unwritten rule when transforming a function into a power series function is that when transforming them into a/1-r you should not change the overall value of the function*, therefore it's preferred to just multiply or divide num/den but when adding a constant, make sure it is =0, just like 1-1 =0, because adding a higher value to make dennominator 1-x introduces a new constant and changes the resulting power series. I got a different answer on my side.
on the last example can someone explain why he wrote one over x plus two instead of -1 over x plus two
the best tutor
What program or tool you use ???
Good luck for you
thank you for this video, very helpful
Thank you so much
Im going to write in "The Organic Chemistry tutor" on the presidential ballot next time around.
does anyone know if you can turn an iterative function into a function? (I'm trying to turn x=x+195y into a function.)
thank you bro
A quick question: When we write Sum (0, infinity) x^n = 1/(1-x) do we include the value x=0 or not?
for example number three why is it only x^3 and not -x^3
for R
The formula is a / 1 - r; the negative in the " 1 - r " is part of it, so you would not include it. However, if it was, for example, a / 1- ( -r ) , you would include it as such.
What if the function you're given is xln(1+x) and the center is at 2? Sorry if this is a dumb question, this is during the COVID-19 quarantine and my calc professor gave up on us. No lectures, just homework that doesn't explain anything.
So is c 0 for the last example? I dont understand how we choose c.
Love from India 🇮🇳 please explain the Taylor's theorem and the expansion of this theorem.
You’re the GOAT
@ 28:01 why is 1/2 * 1/2^n =1/2^n+1 and not 1/4^n+1?
2 * 2^n = 2^(n+1) not 4^(n+1) hope that makes sense. For example try plugging a number into "n" and see what you get. You should understand if you do that :)
Would you agree that 2^2 * 2^3 is 2^2+3 ? it wouldnt be 4^3+2.. Use that analogy.
bicboi46 Or that, I suppose..
You are my hero
Hi teacher, may I ask about one of the examples? 1/(3-x) can also be changed to 1/(1-(x-2)), so a=1, r=x-2
But finally my answer is not the same as yours. The radius of convergence i found is 1, interval of convergence is (1,3).
Am I missing any concepts ?
'cause those of your result that depend on which value of c is given....
this is what I was thinking as well. I do not understand why this is not correct or if it isnt
I. Love. This. Man...
I have a function f(x)=1/(2-x) and i rewrite it as f(x)=1/(1-(x-1) which gives us a=1 and r=(x-1). However in my textbook it says that a=1/2 and r=(x/2)?
Why do you never check the end points for convergence?
For the geometric series to be convergent |r| is supposed to be less than 1 (it’s not
what if my denominator is something like (4x+1)^2?
I think I need to buy a hoodie after all your intstruction masta