❖ Taylor and Maclaurin Series - Example 1 ❖

แชร์
ฝัง
  • เผยแพร่เมื่อ 17 ม.ค. 2025

ความคิดเห็น • 734

  • @patrickjmt
    @patrickjmt  5 ปีที่แล้ว +43

    Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other!
    Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +16

    to find the radius of convergence:
    1) find the length of the interval of convergence (note that you do not have to worry whether the series converges at the endpoints of an interval)
    2) Divide the length by 2.
    That number is the radius of convergence

  • @saraha.mubarak4980
    @saraha.mubarak4980 8 ปีที่แล้ว +264

    It's gotten to the point where I don't think I'll understand anything unless I see a PatrickJMT video about it.

    • @cbaker1514
      @cbaker1514 8 ปีที่แล้ว +7

      omg you just summed up my entire math career

    • @txt0
      @txt0 7 ปีที่แล้ว +2

      This is the only way I can even consider a new chapter/section.

    • @fooyongjie6193
      @fooyongjie6193 5 ปีที่แล้ว +1

      Try organic chemistry channel as well

  • @Bedocalaway
    @Bedocalaway 9 ปีที่แล้ว +107

    I pray everytime I search for a math topic to find your name! & you have no idea how happy I get when I see that your vid is the first result I get :') you're a life savior thank You!

  • @MacieJay
    @MacieJay 12 ปีที่แล้ว +31

    Hope those ads pay you well, you deserve it.

    • @kevininsaurralde6168
      @kevininsaurralde6168 4 ปีที่แล้ว +1

      Now we know how Macie got to be such a smart player.

    • @jordannishi3252
      @jordannishi3252 4 ปีที่แล้ว +1

      The root of Macie Jay's big brain power.

  • @DracutDline
    @DracutDline 12 ปีที่แล้ว +5

    I consider myself quite well off in Calculus, i understand most everything i am presented with, and my teachers have always been quite strong. However occasionally missing a class can put you so far behind in calculus. Bravo to you sir, you take a very difficult subject and make it quite simple to understand online and for free!!! thank you for all the studying time you have saved me.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +1

    glad it helped! i have a playlist on sequences and series as well if you would like to check it out. it is missing a few videos though, so you will probably want to do an individual search for any specific topics. good luck on the next calculus course!

  • @azizkash286
    @azizkash286 2 ปีที่แล้ว +1

    I can't believe I am seeing a video from 14 years ago and benefitting from it

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +1

    glad they are helping! tell a friend or three about them! : )

  • @zackbarlow
    @zackbarlow 9 ปีที่แล้ว +234

    I will owe my degree to you. Thanks man you're awesome.

    • @patrickjmt
      @patrickjmt  9 ปีที่แล้ว +30

      Happy to help

    • @patrickjmt
      @patrickjmt  9 ปีที่แล้ว +109

      Zack Barlow oh, and feel free to head over to Patreon and show a little math love for good ole PJMT

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว +1

    @AceAites you should watch the video on taking derivatives of exponential functions

  • @Captain_Beemo_
    @Captain_Beemo_ 8 ปีที่แล้ว +119

    48 hours until Calc 2 final? Well, here's a video by PJMT, problem solved

    • @MrPlaly
      @MrPlaly 8 ปีที่แล้ว +3

      TEEMO SUX

    • @brikfilm
      @brikfilm 7 ปีที่แล้ว +1

      Did you pass?

    • @user-tm1ix7xi1n
      @user-tm1ix7xi1n 7 ปีที่แล้ว +6

      Jabari Mallory probably failed. You won't pass learning in at the last moment.

    • @tejanb.s1218
      @tejanb.s1218 7 ปีที่แล้ว

      Yasuo OP.... :/

    • @garettmerlino7445
      @garettmerlino7445 6 ปีที่แล้ว +5

      i got 2 hours lol help me!

  • @tashidad
    @tashidad 14 ปีที่แล้ว

    @patrickJMT ---I'm a math tutor who's just getting back into the higher math after 40+ years. I like your presentations and have watched a bunch of them. They are great refreshers.

  • @soccaplaya3303
    @soccaplaya3303 13 ปีที่แล้ว

    I'm taking the Calc BC exam tomorrow and your videos saved my life. They taught me how to do various concepts that I had no clue about in literally five minutes per concept. I don't know how to thank you, but I would just like to say no matter how I do on the test tomorrow, I am truly indebted to you. Thank you so much!

  • @beaniemi8998
    @beaniemi8998 8 หลายเดือนก่อน +2

    This guy is still carrying people's math careers HAAHA. I have a calculus II exam tomorrow and I don't think I would survive without you :'')

  • @jayzeus7
    @jayzeus7 14 ปีที่แล้ว

    PatrickJMT for "TH-cam Educator of the Century"!!!
    You make me a happy human. :D
    You're one instructor who is easy to follow and very thorough. After every lecture, I watch a video by you, to help "drive home" the main concepts. Keep it up man.

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +2

    impressive grade at a young age!! keep up the good work. : )
    and no need to kiss my feet; you are the one who took the tests!!!!

  • @Seanpitcher007
    @Seanpitcher007 12 ปีที่แล้ว

    I'm a chemical engineering student. You got me through precalc, calc 1,2,3 DE, Physics and now a bit of Numerical Methods. You my man have saved me. Nice donation coming when I graduate... starving student now!! Wont forget though. For Gods sake keep it up.

  • @ranger0785
    @ranger0785 13 ปีที่แล้ว

    Yea, gotta agree with everyone else, you rock man. Thanks for doing this, it really is making a difference for a lot of people. I tell people about your videos in every math class I take. I know you make ad revenue off this stuff, but it's still awesome that you take the time to help the little guys behind you. Keep doing what you're doing because there are a lot of engineering, science and math diplomas out there that were granted partly because of your work.

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @EgoWafflez my pleasure!

  • @shamaaz11
    @shamaaz11 13 ปีที่แล้ว

    I've learned more from watching your "series" playlist over a weekend than I have from 2 months worth of calculus lectures....you're my saviour!

  • @kollyman2005
    @kollyman2005 10 ปีที่แล้ว +21

    Patrick is a life rescuer.

  • @sirtwistalot11141990
    @sirtwistalot11141990 14 ปีที่แล้ว

    Very good explanation! Not overcomplicated and not too brief. Teachers always have a habit of trying to instill the entire complicated concept into a student when he/she is just learning the basics, but that comes later. This is a good introduction which can help a student begin to understand the concept of Taylor series.

  • @jancey3
    @jancey3 9 ปีที่แล้ว +3

    You are a lifesaver, Patrick. I was so lost heading into my Cal II final, and then I found this channel and watched your videos all night and I just nailed my final thanks to you. I wish I'd found this channel sooner.

    • @patrickjmt
      @patrickjmt  9 ปีที่แล้ว +2

      +hogfan4-life- spread the word! glad i could help you a bit :)

  • @MexterO123
    @MexterO123 11 ปีที่แล้ว +21

    Thanks Bro. Had to review Sequences and Series in a short amount of time and you just solidified my understanding.

  • @tryhardnoob1140
    @tryhardnoob1140 13 ปีที่แล้ว

    You dont even know how many times its been the night of my homework being due and your videos have stopped me from stressing out and failing my assignments. keep up the good work

  • @xiaostanfirsthumansecond
    @xiaostanfirsthumansecond 6 ปีที่แล้ว +7

    me giving my speech on graduation from college: i would like to thank patrickJMT for helping me pass my classes

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @deadpeng you are correct, not all functions have valid taylor series representations

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    glad you like my videos :)

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +1

    glad it helped : )
    good luck with the class

  • @Tmmmey
    @Tmmmey 12 ปีที่แล้ว

    Whenever I get stuck on a particular topic in mathematics, I utilize the internet to gather information. Your TH-cam channel is one of my top picks. I am grateful for the tutoring in itself, and I like the ideology of free information - using the internet for the best purpose there is. I just donated $10 to you, enjoy the beer(s).

  • @Aboalmaaly
    @Aboalmaaly 12 ปีที่แล้ว

    seriously dude!! when ever i searched on youtube about something in math i find u in the results ... u rock patrick.. thank u so much

  • @guycooper9325
    @guycooper9325 12 ปีที่แล้ว

    I sat through a week or more of maths lectures trying to understand this stuff. Found your video- got it in minutes- you legend!!!!!

  • @berkcan3475
    @berkcan3475 10 ปีที่แล้ว +31

    i am studying for the exam via your videos

  • @patrickjmt
    @patrickjmt  11 ปีที่แล้ว

    that is very kind of you to say

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @myterribletube this stuff provides a super basic way to study and find solutions to differential equations. physics is full of differential equations; they are everywhere. the newtonian laws of motion are differential equations, for example (you do not need this stuff to solve those though). super duper useful stuff. just google it, i am sure you can find some stuff on your own without much trouble at all if you are really interested.

  • @reelgoodfishing
    @reelgoodfishing 14 ปีที่แล้ว

    my friend, you are saving my calc grade. The book we are using is all written in greek symbols and it's very hard to understand and very easy to lose your place. I'm using your videos to review for my Calc 2 exam that I have tomorrow, and who knows, I just might make it to Calc 3. Thank you a million fold. Keep up the good work.

  • @glitterpussss
    @glitterpussss 12 ปีที่แล้ว

    Patrick, my dad asked me the other day who my "study buddies" for classes are. I told him about some of them, "but my favorite is Patrick!" Thank you so much.

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว

    you are right

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @17ashu glad it helped!

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @aznguitar glad you made it through your class!

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    my pleasure!

  • @cameronmx9
    @cameronmx9 12 ปีที่แล้ว

    You sir, are the man! I have a calc 2 test tomorrow and was lost earlier this week before discovering your videos! Confidence goes a long way with this stuff, and you sure do a great job of providing it.

  • @josephmendoza4390
    @josephmendoza4390 6 ปีที่แล้ว

    10 years later and still the most informative and easy to understand math youtuber on here

  • @Andrew-pu6zb
    @Andrew-pu6zb 12 ปีที่แล้ว

    Man, just letting you know .. you are a life saver!!! ... I watched all your videos about series for over 3-4 hours straight the day before my test... on my way to the test i felt like i know nothinnnggg and during th test it was even worse ... i just received my grade .. i got 88% ... thaaank you for reprogramming my brain lol

  • @jakxon325
    @jakxon325 15 ปีที่แล้ว

    if only u were my lecturer for maths. I'll always look forward to go to your lectures. i will not miss a lecture, even if I only have 1 lecture that entire day and having to travel 2 hrs to get to uni. Because you explain things so clearly and easy to understand!

  • @GAment_11
    @GAment_11 4 ปีที่แล้ว +2

    I started college back in 2008 knowing minimal about Math. Through the years, I like many have watched your and others videos which have got me to where I am today. In 2020, I am back at it, and studying Robotics. It is nice to revisit your well put together content. Thanks for in many ways being someone very memorable to my, and most likely many others, academic career.

    • @patrickjmt
      @patrickjmt  4 ปีที่แล้ว

      congrats! i always wanted to get into robotics but never did. have fun with it, it sounds fascinating!

  • @lolbenjay
    @lolbenjay 9 ปีที่แล้ว +1

    you are the only person that explained when you set a variable to the other side of the equal sign you are awesome

  • @liliwang9950
    @liliwang9950 5 ปีที่แล้ว

    I went to his website and I was so impressed by that bunch of free videos... This man is really, really amazing!!

  • @ecgimenez
    @ecgimenez 14 ปีที่แล้ว

    you make my day! i was reading my textbook for my final tomorrow and was ready to pull an all nighter. then i came across your videos and understood all these so fast! much much less worried now!

  • @Shankovich
    @Shankovich 10 ปีที่แล้ว +4

    Thanks man! Taylor expansion came up for a formula in aircraft dynamic stability and I needed a refresher. Video was WAY faster than pulling out my calculus text hahaha.

  • @JGulickx
    @JGulickx 11 ปีที่แล้ว

    I've been looking at my book for hours, and i didn't get it. After I watched the first 2 minutes of your video, everything was suddenly clear! Thank you sooo much for this video!

  • @narekkazarian4943
    @narekkazarian4943 11 ปีที่แล้ว

    I've been watching your videos for several years and I can safely say that you and Khan (KhanAcademy) are the best teachers I have had the honor to listen to and take advice from.
    Thank you.

  • @kishaihd
    @kishaihd 10 ปีที่แล้ว +4

    ... I've been struggling with this for a week, and this video made it make sense before the 2 minute mark.

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    u are taking it now! goooood luck!

  • @pbrocket296GT3
    @pbrocket296GT3 3 ปีที่แล้ว +1

    I just felt like going back to this video today not to review but more like a "throwback". Thank you for helping me throughout my engineering degree Patrick 3 years ago. Also, I recently have written a shell script for this in case. Much appreciated again man!

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    ha! well, i am sure your teacher was answering questions, doing more examples, and going into much greater detail : ) - thanks though! i am glad my 10 minute explanation helps!

  • @ThePiperSwapper
    @ThePiperSwapper 12 ปีที่แล้ว

    Calc II is made easy with your informative videos. I personally thank you on behalf of all students in that you are willing to take the time to make a difficult topic easy to understand. I've been using these videos to help through Calculus II in my Freshman year of college and they make my exams (60% of our grade) relatively easy. Keep up the awesome work! Thanks.

  • @poserlooser
    @poserlooser 16 ปีที่แล้ว

    Thanks for this video, it really clarified the Taylor series stuff for me..and leaving the terms as 5^2, 5^3, ...5^n is a really smart thing that I hadn't been doing...it makes coming up with the summation notation allot easier in harder problems.

  • @jayisfresh1990
    @jayisfresh1990 15 ปีที่แล้ว

    These videos are great. They really help supplement my teachers lectures. I'm pretty sure the only reason i have a chance at passing this calculus class is because of your videos! Thanks for putting these up.

  • @nehellenya9633
    @nehellenya9633 9 ปีที่แล้ว

    Srsly, who downvotes this guy's videos? This guy is helping thousands of people understand what at first appears to be gibberish. I watched these vids before my Calc exam. Saved my life.

  • @shenreon
    @shenreon 7 ปีที่แล้ว

    2 years into my Chem Eng. degree, and this man has saved my ass numerous times already. Writing the last Calc final I will ever write for the rest of my life tomorrow. Thank you so much for your videos!

  • @matticus409
    @matticus409 12 ปีที่แล้ว

    my professor tells us "watch videos on youtube" and sits at his computer and surfs the web. Nice way to go though calc2, huh?
    You are a godsend!
    you have taught me more in the past 7 mins than my professor has taught me the whole semester...

  • @millenniumf1138
    @millenniumf1138 13 ปีที่แล้ว

    Wow! You explained in six minutes what took my professor a 50 minute lecture to explain! I've got a calc quiz tomorrow, and this has been very helpful! :D

  • @ian559fresno
    @ian559fresno 13 ปีที่แล้ว

    You are a legend at my school. Everytime someone's struggling like math we hear "Watch PatrickJMT videos" haha

  • @vaku66
    @vaku66 16 ปีที่แล้ว

    I would seriously recommend you for any Calculus teacher position out there. We had to learn these ourselves, and just by quickly reading over a textbook and watching this vid, i learned them no problem :D
    Thanks!

  • @Reality_loser
    @Reality_loser 12 ปีที่แล้ว

    thank you so much for making these videos. I cannot stress enough how much they've helped me get through this quarter of calculus, without these videos I'd most likely be failing. Thank you so much! Donating now.

  • @taylor914ce
    @taylor914ce 4 ปีที่แล้ว

    I just wanted to say thank you. Your videos saved me from failing my calculus class back in december 2008, and I even used some of your techniques when I teached calculus in 2017 and 2018. Again, thank you very much.

  • @xvillalon1
    @xvillalon1 14 ปีที่แล้ว

    Thank you! Math prof gave me a hard time because I asked if 1! and 2! when he wrote just 1 and 2 should be understood, but nice to have someone take the time to really explain!

  • @joshuaparina6915
    @joshuaparina6915 12 ปีที่แล้ว

    Thank you very much for your videos. I had an F going into spring break, then I found your videos and passed the class with an A at the end of the semester. Keep up the good work sir. It is very appreciated!

  • @olonnns
    @olonnns 11 ปีที่แล้ว +2

    Wow this video really helped me understand Taylor and Maclaurin series for the first time. I had trouble learning from the book and from my teacher but this really did it. Thank you so much! You did an extremely spectacular job at being clear.

  • @tipoupee2000
    @tipoupee2000 14 ปีที่แล้ว

    You make this stuff so easy to learn. I missed a couple of classes in my college calculus class and you help tons! Thanks a million :)

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    nice improvement!

  • @Alex-bc3tt
    @Alex-bc3tt 10 ปีที่แล้ว +35

    STRAIGHT TO THE POINT, I WISH I SUBSCRIBED EARLIER

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @FaiththeHairstylist no, no, it would make to much sense to look it up. it is much easier to post a question online and then go back to watching justin beiber and hold one's breath until getting an answer

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @gaboonviper89 lots of sequence and series videos, so come back any time : )

  • @enaba2006
    @enaba2006 16 ปีที่แล้ว

    You rock!! may good blessings always be with you! you have no idea how much this means to me! I have a midterm in a few hours, and believe me this helped me ALOT!!
    Million thanx to you!!!!!

  • @tiaramcdonald9209
    @tiaramcdonald9209 12 ปีที่แล้ว

    You are more than awsome...I have been watching your videos since high school and im a freshman in college and Im still watching you..thanks a bunch!

  • @kengking2708
    @kengking2708 9 ปีที่แล้ว +1

    couldn't believe after 4 years later I'm still referring to your videos. There's no other explanation simpler than yours, I don't know why professor and phd lecturers should still be teaching...

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว

    wonderful, glad you nailed it : )
    i tend to pick out good examples, in my own humble opinion : )

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @ian559fresno that is very nice of you all, i appreciate the love :)

  • @sgtgs42
    @sgtgs42 14 ปีที่แล้ว

    How can you explain to me in 10 min what my math professor can't do in 3 lectures? You must be a god!

  • @DRMRBOY92
    @DRMRBOY92 13 ปีที่แล้ว

    Patrick, I just finished watching your videos in preparation for my calc. 2 final tomorrow. Thank you so much for putting all of these extremely helpful videos up on youtube. I now know I can do well because of you. :D

  • @Nuviremus
    @Nuviremus 15 ปีที่แล้ว

    This video also cleared up quite a few issues I had with doing Taylor series problems. Thank you.

  • @lolno6527
    @lolno6527 8 ปีที่แล้ว +1

    This explanation was way better than Khan Academy! I am surprised this page is not verified yet wth! Patrick you're the Lord of Maths man!

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    glad it helps!

  • @ismailniyaz5167
    @ismailniyaz5167 5 ปีที่แล้ว

    I managed to study everything I needed for my Calculus course in less than a week via this channel. This after having been struggling with the textbook and not making any progress for the last six months!

  • @Diogie12
    @Diogie12 12 ปีที่แล้ว

    you are awesome omg. i've been trying to figure this out for hours from just reading the book and my notes and nothing clicked before i watched your video.

  • @smilesrfree85
    @smilesrfree85 12 ปีที่แล้ว

    I absolutely adore your videos! They are such a help when trying to go back and figure out what the heck the professor skimmed over.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    thanks!

  • @beyondbirthday4212
    @beyondbirthday4212 3 ปีที่แล้ว

    I was 6 when this video was released and now I am at engineering and that is helping me significantly more than professors.
    Proud of you

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @PCGamerPortal that's what she said

  • @iamkevinthecanadian
    @iamkevinthecanadian 11 ปีที่แล้ว

    10/10 for the pun in the annotation. It was a much needed smile during my studying.

  • @bulgaboi
    @bulgaboi 11 ปีที่แล้ว

    These videos have helped me semester after semester. Engineering is tough and I'll take all the help I can get. Great videos.

  • @EmceeDG
    @EmceeDG 14 ปีที่แล้ว

    Wow thank you so much, I was literally about to tear up trying to understand this before i came across your video. I know you might not know me or anything, but wow your video shows real dedication to teaching, and for that I am truly grateful.
    thanks for much!!

  • @ktrealty96
    @ktrealty96 9 ปีที่แล้ว

    You are the best at what you do ! I just wanna say I really appreciate your videos because without them..idk what i'd do.Thank you !

  • @yukun92
    @yukun92 13 ปีที่แล้ว

    Thank you so much. Your videos are really making calculus much easier for me and what seems like thousands of others. What will we ever do without you? :)

  • @NateTheGreat555
    @NateTheGreat555 13 ปีที่แล้ว

    Everything just seems so much simpler in these videos. Great help for my calc test tomorrow!

  • @darkdopple9333
    @darkdopple9333 15 ปีที่แล้ว

    man I'm so glad I found your videos, this is going to help me a lot for my cal 2 final tomorrow.

  • @Salmounaaaaxox
    @Salmounaaaaxox 5 ปีที่แล้ว

    Less than 24hours before call 2 final exam , Patrick you are a life saver no cap! Wish me luck!