Taylor's Inequality

[tashfiq1993]

very helpful video, helped me on my midterm and now its gonna help me on the final lol

I just hate the fact that theres an ad in the middle of the video....

[jburt1992]

Great job with the videos. Minor correction, though: at 10:34, (.0016) should be to the (n+1), or 4th power.

[andreluxury]

a good tip to understand it is to actually work out the problem as he is doing it as opposed to just watching

[mytwohands]

Oy this is still confusing. *time to watch it again*

[patrickJMT]

@mytwohands i always found this to be confusing as well. i think most people do. it is something that a lot of people ask about when i used to tutor a lot

[Arwokid]

seriously, what does mormans have to do with calculus...>_> (referring to the annoying ad on literally every every 2nd patrick's video)

ffs at least alternate the ad or something. im trying to learn not convert

[eowdaoc]

Fckin ads.

[dagarciawmedu]

This is the first video I have found on the subject. Thanks for the lecture. Now I am more prepared to go to class and talk about this stuff.

[corkery12]

good job on the videos patrick! They've been a great help, you're the man!

[jw111892]

i feel this is almost the same as alternating series estimation

[Feduchi2010]

At the end you wrote a 51 instead of 56, just letting you know ;)

[erwinthehamsandwich]

Yo, Taylor. I'm really happy for you, I'mma let you finish but Pappus had one of the best mathematical theorems of ALL TIME.

[tupacsomething69]

@erwinthehamsandwich pretty sure pythagoras did

[maggen1000]

I don't write youtube comments very often but this guy deserves the thumbs up

[breathnac92]

gory details LOL!



[powerseriesman]

correction, i guess its in my book that formula. but i prefer the the formula with c in it.

also your argument that lim x^n+1 / (n+1! converges to zero is flawed. the reason is because each x is a constant inside that expression relative to the index n. and lim k^n / n+1! converges as n-> oo

[powerseriesman]

whats with the | x - a | < d.

You're not even using the correct taylor remainder formula. it is

Rn(x) = f^(n+1) ( c) (x-a)^n / (n+1)! , where c is between a and x . Now x can be greater than a , or x can be less than a, so you have two cases there.

[Jruberti]

I just wanted to thank you master patrickJMT. I managed to get an A in Calculus II thanks to your vidoes/iphone app. Your brain/videos rock!

[joplimat]

What the heck is M? What defines M?

[hogs46]

@joplimat

I think it's your (n+1) derivative of your original function. But i really dont know

[ac7491]

15 professors hate that you divulged their secrets

[1ordofsarcasm]

Thanks for the vid! Could you put up another example of this? It's a little complicated and having another example to follow would be amazing!

[wukuanlin]

FUCK MORMONS, I WANNA LEARN MATH.

[jakeyboyGH]

@wukuanlin FUCK YOU SERGIO SANCHEZ

[zoom2121]

@jakeyboyGH lol Piece of shit advertisement, but we shouldn't complain.

[jiamonx2]

how come at the end you don't have a negative beside the 56/81?

[kramzize]

you're a lifesaver. thank you so much. i've been doing this for 2 weeks in class with no success and all it took was fifteen minutes of your videos to make me understand it. much appreciated!

[Ew0kHunter]

I love you, i have a calc 2 final in 30 min :)

[physicsgod94]

Dude, why don;t you teach? I swear my calculus BC teacher is a death eater. Come to NC

[rysticblade]

Truly appreciate the video!

[DocileRaptor]

Last part - you made it 51/81 where it should be 56/81

[crizl2007]

forget it, I found my error!

[crizl2007]

at 9:21, the value shoudln't be 1.2 instead of 0.2? Or am I confusing something? 1.2 is the biggest number in the interval...help!

[dhcrazy333]

@crizl2007 |1.2-1| = .2

|.8-1| = |-.2|

[yumigator]

Thanks for this explanation, it'll be a big help on my exam tomorrow

[Zims63]

you helped me pass a test man. thanks.

[ironicRON]

lol you wrote 51 instead of 56 in the end

[MrStefan9610]

At 10:20 when you sub the derivative back into the equation, is the R3 supposed to be less then -(56/10)? you made it positive but was that by accident or is it an absolute?

[lancevancedance]

come teach at michigan state! we need ppl like you who actually TEACH! the fate of the future's engineers lies in your hands :D

[hobokook]

i love you

[Twentydragon]

I don't understand what you did at 7:30.

[kingk1000]

@Twentydragon he just subed the values 

[charlesc300]

you should be teaching at u of i lol

[RaniOfCoochNahi]

If I could I would give you a bouquet right now because I ACTUALLY GET IT! For once! :D

[twirmd]

You use the Stewart calculus book :3

[jacob1326]

Just wondering what one should be recognizing/noticing to come up with "Rn(X)" for any given function (other than your examples).

Also, when evaluating an inequality with a value on the given interval, should your intention always be to maximize the right side?

(not as important)

[tucense]

MATH IN PERMANENT PEN? Beautiful..

[timmy69690]

Can it happend that the 2 valuea of x arent the same for both condition to make the value larger as possible?

[psychofish25]

hey thanks so much! i'm a college freshman in my calc 2 class, and while i've always been a math geek, my textbooks explanation of this was plain terrible. thanks so much for a great tutorial. keep up the good work!

[mailmepizza]

My book speaks Greek but you speak English. Many thanks my friend.

[Decessus117]

How the heck did Taylor figure this out, anyways? I mean, it just blows my mind.

[patrickJMT]

@Decessus117 the 'why' is always more interesting than the 'how', i agree!

[harilikeawavinflag]

thanks

[lancevancedance]

@Decessus117 try to imagine how brilliant this guy had to be to CREATE this process. smh :O

[imjohn007]

fuck 11 people who disliked this video

[patrickJMT]

@imjohn007 bitches

[sjsawyer]

@patrickJMT lmao

[kSonico87]

Man...I don't know who Taylor is, but I'd like to shake his hand. Thanks PatrickJMT.

[shamnTM]

Hi Patrick,

I would like to merely point out that the Taylor Inequality you have used to estimate the error bound is only applicable from the interval [0.8, 1]. If you estimate any value between [1,1.2], you actually obtain an alternating series. The estimation for the error bound of an alternating series is the next term omitted. Hence, the error bound you have calculated does not apply for all values of x on the interval, but only from [0.8, 1].

[raspberrysky294]

This is really great! I was totally struggling with Taylor's inequality until this, and I'm pretty good at math!

[ryezizzle]

i'm confused. shouldn't the inequality be |x-a|^ n+1

??

[ryezizzle]

@ryezizzle

oh nvm, n = 3 sorry

[ryezizzle]

my professor could spend months on this, but u pretty much summed it up in 10 min. keep it up

[jieun7543]

the first time i watched this video i didnt quite understand it... but watching it over and over, i finally got it! :) thankyouuu

[dragateli]

this is awesome! Could you explain tho, while you are getting the remainder, why you used .2 and not 1.2? thanks

[jieun7543]

@dragateli i think he used .2 because that's the biggest value that you can get for abs(x - 1) when you plug in the numbers in intervals [.8,1.2] obviously you wanna plug in .8 or 1.2 for x. and when you do that, the value inside the absolute value sign would be .2 ... sorry not very good at explaining~ hope u understand what im talking about..

[dragateli]

@jieun7543 ohh

so he did use 1.2 :P sorry I was up really late studying at 4 am haha 1.2 - 1 = 0.2. Doihhh haha. Thanks :)

[Wushu360]

Best Austin Math Tutor indeed!

[lifematch]

i honestly think you should get the Nobel Prize of education or something!

[Starrynova]

I love you man

My prof made this terribly confusing, and you showed it doesn't have to be!

[appppppppple]

how come my teacher said that in an alternating series

the remainder is less than or equal to the next term

like this problem we had

f(x)= e^(-2x^2)

g(x)= is the sum of the first four nonzero terms of the power series for f(x) about x=0. show that |f(x)-g(x)|<.02 for x: [-.6,.6]

O WAIT NEVER MIND I UNDERSTAND

ITS CAUSE YOU HAVE A VALUE AND ADD OR SUBTRACT A SMALLER VALUE FROM IT SO THE ERROR IS SMALLER AND SMALLER

maybe not though?

[PrisonbreakCB]

Hi Patrick, Great VIDEO!

Why did you sub 1 into your f's and derivative f's?

What is the purpose of d like WorldCollections said?

[jieun7543]

@PrisonbreakCB he sub 1 into f's and derivatives f's because a= 1 (given)

[WorldCollections]

Hi. What does the letter d represent in Taylors Inequality ? BTW...great video !

[interxavierxxx]

Hi Patrick,

Is the Taylor's inequality applicable in all cases? In my textbook, the example (which is quite similar to yours) used the alternating series estimation theorem, not taylor's inequality.

[justin896]

I agree with everything Bloohaha said and more, thanks for putting so much time and effort into maintaining online videos for such a wide variety of calculus concepts. Now if only there was an online tutor this excellent for my linear algebra course >.O.

[Bloohaha]

Amazing videos patrickJMT, I watch them all the time (even when I'm not struggling with a concept), just because you make concepts easy to approach, manage, and understand.

[patrickJMT]

@Bloohaha thanks : )

[achironis10]

at 10:30, how did 56/81 turn into 51/81?

[unknownlove19]

@achironis10 its just a mistake.

[jamespb20]

Thank you very much. Your videos are etremely helpful!!! Please keep your great work!! It does make a difference!!

[Kalbert138]

Thank you so much for this video. Helped me understand the last part of my calc homework. I see you have many other videos so I will check these out when I need to!

[mmmocto]

You. Are. Amazing!

[tkdmaster3bd]

keep posting these, man. these are so helpful.

[athmi100]

These videos are so helpful...Thanksyou :)

[noronahahaha]

aren't you finding the derivatives for f(a), not f(x)?

[briantexts]

Has to be the most difficult thing i have learned in calculus thus far.

[BeeTeeBeeAyEm]

yeah, our teacher said that this was the hardest stuff we'd do all year, but once you get it, it's not too terribly difficult.

[Moollaman]

Amazing videos, just wanted to let you know you should add this video to the Sequences & Series Playlist, just watched them all and noticed this one was missing. Now I understand calc so much better.

[vs127739]

You should explain why you took 1.2 on the right end instead of .8 at the left end to the |x-1|^4 ----> to yield |1.2-1|^4 which implies |.2|^4 . Explain that you took 1.2 because the function f(x) is increasing. You would use .8 if the function was decreasing.

[Tunassassin23]

You're amazing! Thank you very very very much!

[spagettboopbeep]

thank you so much

[Timbeon]

...I THINK I GET IT NOW. Thanks! 8D

[Tetsuo2009]

yeah, papaya seed dressing it tops.

[RICbass78]

i was sorta confused till the end, but thanks for the help!!

[moreoriginalusername]

when you plug in (0.8) into the 4th derivative of f(x) why is the coefficient (56/81) and not -(56/81)?

[crazylike6]

thanks, that was really helpful

keep up the good work!

[slaskpost1]

I wish you were my brother or something so I could get private lessons every day :D You are awesome!

[sandyloowho5]

really helpful! keep up the great work =)

[SlimShuvro]

Great Video Broskii! I have a calc test tomorrow and I missed a whole bunch of classes, hopefully I'll do well due to your video. You are the man!

[kcbanner]

you rule. keep it up man, good shit.

[soccerboy1016]

No inspiration, he meant to write 56, he even said it aloud. Great video

[inspiration4him1]

At the end you used a 51 instead of 56 in the previous part of the problem. Is this an error or on purpose?

[jeremygballa]

thanks broseph.

[UjjawalManocha]

umm Patrick.. at the end i did not get how you could plug in different x values to maximize the different components of the inequality. like for one you plugged in 0.8 and the other you did 1.2

[SlimShuvro]

I had the same question, anyone have the answer? I've seen someone else do this in a problem as well, and it didn't make intuitive sense to me.. :(

[gunnersquirrel]

Patrick, you are a god amongst men

[gtech90]

Thank you! This has helped tremendously with my calc II course. :)

[sinusitiscap]

You saved me again man!! I was daydreaming about salad dressing when the prof was covering this in class so your video made all the difference for me.

thnx again!!

[kcbanner]

I love salad dressing!

[patrickJMT]

there is this really good papaya dressing i like to eat.

it is my favorite.

that and blue cheese.

and i also like balsamic vinagrette too.

[Erichitown]

@sinusitiscap Haha oddly enough i was daydreaming about salad dressing during the first watch of this video. great video though

[maraxus94]

Thank you sooo much! I had a test on infinite series and all that jazz and thought I was for sure going to fail it while I was studying. That is, until I found your awesome videos. I watched them for about 4 hours straight, and all of a sudden everything made sense and I got a solid B, which I am quite happy with given the course. I referred you to several of my friends, so keep up the good work!

[patrickJMT]

thanks, glad the vids helped you out : )

[skyfireninja]

i really appreciate the videos.

they are extremely helpful when it comes to reviewing a tremendous amount of material for the final.

thank you!

[Leonidus0]

at 10:22 you wrote 51/81 .. do you mean 56/81?

[nmullins20]

ya he even said it out loud.

[patrickJMT]

thanks : )

[greenelephante]

your videos are AMAZING! i really appreciate the help... is there anyway that you could do a video of a taylor's inequality problem when you know the desired error and value of x but need to find the number of terms to get it within that error? or do you know where I can find any of these problems worked out

? THANKS!

[Frisbeedude2391]

THIS HELPED SOOO MUCH!!!

[patrickJMT]

good : )

[cricketboxer]

thanks a lot :D

ur explanation is great

[loempiaaaaa]

uhmm this actually helped me quite a bit! thank you.

[whenultra]

q if|x|=x/4*x'2 can M ever equal a parrelel geometrical array as infinite geometrical sequence, as pi * x as x/24 the x=x*1,x*2,x*3,... then v=x*pi (where v is a volume)

[leroy337]

no problem

[driftx2]

At 9:36, isn't it 1.2?

[sofaking008]

I just noticed that... I think it is suppose to be 1.2, and it would be = 2.0736 thus the answer in the end would be aprox .028391175

can I get a confirmation?

[leroy337]

No it's 0.2. The largest value that |x-1| takes on the interval (.8,1.2) is when x=0.8 or when x=1.2 ( |0.8 - 1|=0.2 or |1.2 - 1|=0.2 ) thus he is correct and it would be .0016

[sofaking008]

Ahh... I see now. Thanks for clearing that up.

[patrickJMT]

yep! thanks for helping out leroy!

[Kmwiti]

I was just wondering whether at the 2:30 minute, it's meant to be Mclaurin Inequality and not taylor inequality since a=0? .Thanks for your videos.

[patrickJMT]

nah, it is called taylors inequality, after taylor!

a maclaurin series is just a special type of taylor series anyways

[beefwingers]

amazing video - thank you so much

[patrickJMT]

no problem, hope it helps!

[ash3231]

thanks so much!  that helped a lot and now I'm off to office hours and I won't look too stupid now!

[patrickJMT]

ha!

[nickst4z]

Just out of curiousity, what level math is this in America.

But THANKS HEAPS patrickJMT this reallly helped me out

[patrickJMT]

calculus is typically taught starting at around 10th grade (if the student is good) through college obviously. i did not see this stuff til i was at least a sophomore/junior in college though, as i did not take a lot of math in high school, or when i first got to college either

[joeschmo88]

im still having trouble understanding taylor's theorem for you second example. can you do a problem that has no interval? thanks!

[waytoomanyjoes]

instead of just saying "you should know that factorials grow faster than exponents" which could get mixed up under time pressure, another way to know that the limit of Rn -> 0 is if the series convereges, since all series that converge have a limit -> 0, this can be done fairly quickly with the ratio test, just to check. Thanks for making these videos!

[patrickJMT]

good point! i think that is another good way of remembering it. thanks for the helpful comment

[Cryptlord91]

Do you have any videos on solving polynomial inequalities with one variable?

[patrickJMT]

yes, there are quite a few inequality videos on my website

[PedroPedroPedrao]

waytoomanyjoes, this is not correct. He is correctly verifying that the series converges to the given function. And Taylor inequality is necessary for that.

In order to verify the series converges, ratio test is enough but then you dont know for which function it converges.

[sammem1]

that helped me thanks!

[ContraWagner]

Great video!

[patrickJMT]

Thanks!!

[patrickJMT]

at the end, i right down 51/81, but obviously it should still be 56/81! likewise, the negative gets dropped due to the absolute value in taylor's inequality. i had to speed up so that i could post the vid here! : )