Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: th-cam.com/video/PmHaNjDBh_c/w-d-xo.html
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'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!
@@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...
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!
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.
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)?
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 ?
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???
In 8/(2x-9), why can't we just divide each term by 9 to get the 1 - r form? That method gives me an interval of -4.5 to 4.5. Is that the correct way to do it?
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
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 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.
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
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 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!!!!
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.
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)
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.
reviewing this for some higher level stuff that requires taylor series. At this point, I love math... but when he said partial fraction decomposition, I had some serious PTSD.
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.
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.
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?
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: th-cam.com/video/PmHaNjDBh_c/w-d-xo.html
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 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'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!
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.
i'm taking my calc 2 final today and i've been on ur page ALL DAY, hope it pays off
Did it?
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!
My god, thank you! Gotta love struggling in the hardest unit of the hardest calc class...
Infact this man is a hero❤❤❤
there is one thing to say about this video, 'LIFE SAVER.'
Man, you're a lifesaver
Ridiculously good video.
you r a good man...
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.
Thanks!
U saved me ❤ i survived god bless u ❤❤❤
His voice is nostalgic
You saved my life
You are my hero
My final is in 3 hours, wish me luck i will need it
Are all power series representing a function have an open interval or do we have to test the endpoints in every problem?
I think I need to buy a hoodie after all your intstruction masta
If frustrated with classes, try speeding up to 1.25%
Thank you so much ❤️感謝你
In the last example can not I just use completing square in the denominator and solve it as the previous examples ?
I LOVE YOU!!!!
what if my denominator is something like (4x+1)^2?
Thank you!
thank you
Uliwakulefye boi my degree will be in your name 🙌🏾
DRIP OR DROWN FUTURE ENGINEERS WE MEET HERE TO OVERCOME THE GRAND OBSTACLES PRESENT IN OUR ACADEMIC CAREERS.
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"
Thank you sooo much!
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)?
at 49:30 isnt the 1/x+2 negative?
Yeah it is
Why did I ever decide to take AP Calculus BC 😭
I ask myself this on a daily basis ughejfkdj
@@michellemiao_ Ugh same this class is too much for my small brain T ^ T
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
how can you be sure that |-x|
22:00
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.
28:45
Are you a doctor ? Cause all you do is save lives !
38:39
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
In 8/(2x-9), why can't we just divide each term by 9 to get the 1 - r form? That method gives me an interval of -4.5 to 4.5. Is that the correct way to do it?
CALCULUS 2 TATE 105 💯
So what problems do you have to test the endpoints for?
bro gud job!!
I got a test tomorrow...ohhhhhhhhhhhhhhhh boy...
29:00😅
That one of 8/something it's wrong
cool
Those questions never come in the exam to be honest
It’s 1am and my cal II final is at 7:30am. Wish me good luck by liking my comment lol
I liked most of your videos but I absolutely hate this video of your's you made me so confused on this chapter. other explain it so much better.
I did not like this video
pog video
I make a lot of calculus 2 videos on my channel please check them out.
Appreciate any support
can anybody help me with this one: (x+1)/(x+2)
Idk about other ppl but I feel like Calc 2 is joke easy compared to calc 1
I'm so low IQ lol i dont understand whats going on
In sum of powers series prove aₙ ➝ 0 please solve
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
thank you!
watching 1 day before final exam
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".
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 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 ^
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
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😂
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 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 dont care I just want a fucking formula i can pump my fucking numbers into and forget about this
i 100% know how you feel
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.
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
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)
God bless you, man 🙌🏼😭. you doing God’s work out here by helping us struggling students.
Any one with exam tomorrow? (me)
Yup
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.
I wish our dear lecs could copy OCs method of content delivery.
Im going to write in "The Organic Chemistry tutor" on the presidential ballot next time around.
reviewing this for some higher level stuff that requires taylor series. At this point, I love math... but when he said partial fraction decomposition, I had some serious PTSD.
Woah you teach everything from math to chemistry
Damm
Thanks a lot
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.
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!
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
Awesome work JG! Just when I thought I conquered all algebra, it took Calculus 2 to teach me more algebra =)
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.
thank you bro
on the last example can someone explain why he wrote one over x plus two instead of -1 over x plus two
at 30:30 was the negative factored out wrong or am I missing something?
thats what i was thinking too
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.
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?
This is easily the hardest part of calc 2. Thank god I did good in the other chapters so my grade can afford it
Excellent. I Feel like I'm ready for the mathematics olympiad
Hello please when you make it next time please be quick because we have lots of things to do after the video 😢😢😢 please
goat
this is all good material, but now how do you deal with functions like sin(x)? :)