Taylor Series of ln(x) at x = 2, calculus 2 tutorial

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  • Опубликовано: 2 июн 2016
  • Taylor Series of ln(x) at x = 2, problem from James Stewart calculus.
    Need to prepare for your calc 2 final? Check out my "100 Calculus 2 problems ultimate review" 👉 • 100 calculus 2 problem...
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Комментарии • 87

  • @97jumpstyler97
    @97jumpstyler97 7 лет назад +185

    when an asian who speak engslish is more understandable than the proffesor who speak your native language.
    good job man

  • @py2396
    @py2396 4 года назад +8

    Wow you made this question so easy, thank you so much! Honestly I couldn't have survived my cal course without this channel.

  • @bartibox
    @bartibox 6 лет назад +10

    Thank you so much! I'm a student from Poland and you explained it so clearly that non professor at my university!

  • @XxRaunxX1215
    @XxRaunxX1215 7 лет назад +49

    Thank you so much! This was explained so much clearer than how my professor explained it!

  • @svmafnas
    @svmafnas 7 лет назад +5

    Great, clear explanation!! Thank you so much! I know I'm gonna do well on my final now! Keep it coming!

  • @wardbeehre773
    @wardbeehre773 7 лет назад +10

    THE OOD MIC IS AMAZING!!!!

  • @borg972
    @borg972 7 лет назад +22

    where is the explanation about finding the radius of convergence?

  • @jessicaramer6630
    @jessicaramer6630 2 года назад +1

    Thank you for this clear video that has answered most of my questions. Great job.

  • @patrick_tostes
    @patrick_tostes 5 лет назад +2

    THANK YOU MAN YOU DONT KNOW HOW YOU HELPED I LOVE YOU SO MUUCHH

  • @____Paul____
    @____Paul____ 3 месяца назад

    You make learning math enjoyable! Thanks so much, I hope you make lots of money through this channel!

  • @cosmickitty9533
    @cosmickitty9533 8 лет назад +2

    THANK YOU!!!!! Im watching all of these!

  • @carolinavendano
    @carolinavendano 4 года назад +1

    Thank you kindly! your explanation made it all incredibly clear.

  • @OPP534
    @OPP534 3 года назад +1

    your best work yet!

  • @jackearhart4265
    @jackearhart4265 5 лет назад +1

    youre awesome I don't know how i haven't seen your vids before

  • @mmka5434
    @mmka5434 7 лет назад +1

    Excellent explanation! Thanks!

  • @cetinz4848
    @cetinz4848 3 года назад

    Best video on Taylor series out there, holy

  • @blazegg8209
    @blazegg8209 3 года назад +1

    This is a new facial hair combo for me. Very exciting after so many videos!

  • @blue_light_bot
    @blue_light_bot 2 года назад +1

    awesome explanation, thank you!

  • @josephinemartin
    @josephinemartin 5 лет назад

    Thanks so much really helped me understand the concept

  • @dr.rahulgupta7573
    @dr.rahulgupta7573 3 года назад

    Thanks a log ( base e) for beautiful explanation . Dr Taylor Series .

  • @Muro-qm8xo
    @Muro-qm8xo 4 года назад +2

    you are amazing and neww beard, that looks really good mashallah brother :)

  • @Ivan-mp6ff
    @Ivan-mp6ff 4 месяца назад +3

    No one properly explain what (x-2) represent. Is it a shift of the curve by 2 units to the right or we are taking derivative at x=2 on the original graph. Mechanically applying the formula is not important. Contrasting it to expanding (x+dx) is another confusing aspect of Taylor expansion.

  • @jamesacosta6090
    @jamesacosta6090 5 лет назад +3

    so where is the video where u show how to get the r=2?? u said the next vid, but the next vids isnt it. thank you in advance.

  • @mariomario-ih6mn
    @mariomario-ih6mn 4 года назад +7

    I search up t-series on wolfram alpha. Taylor series comes up.

  • @Shk4You
    @Shk4You 8 лет назад +3

    error calculation exercises of taylor plss

  • @gloystar
    @gloystar 6 лет назад

    Can you please make a video deriving the Taylor series for sqrt( 1 + X ), around X=0. I'm curious how can we derive a pattern for this, seems so difficult. Anyway, very nice video man! I enjoy your videos.

    • @user-nx8fg9ny8i
      @user-nx8fg9ny8i 5 лет назад +1

      It's just like that: 1+(x/2)-((x^2)/8)+((x^3)/16)-((5x^4)/128)+((7x^5)/256).... and so on, i hope you will see the pattern and continue it yourself. If not, then try do Taylor series for easier functions

  • @wendyk4775
    @wendyk4775 6 лет назад +1

    awesome!

  • @barryhughes9764
    @barryhughes9764 5 лет назад

    blackpenredpen. Any chance in the future as to 'why' the Taylor series works, the intuition behind it? How does taking successive derivatives approximate a function? It is not sufficient to learn by rote without understanding the underlying concept. As far as I can discern it has something to do with 'rates of change of the function mirroring the rates of change of the series approximation about a point, and whether that that rate of change is positive or negative. Any lucid explanation would be gratefully appreciated, and thanks.

    • @tcris45
      @tcris45 5 лет назад +2

      You could search for 3brown1blue's it has a nice series about this topic

    • @barryhughes9764
      @barryhughes9764 5 лет назад

      Tudor Cristian. Thanks for your advice, since asking about this I have actually watched 3blue1brown and it has indeed answered my questions regarding this topic. The concept and intuition behind the 'Taylor' series is clearly explained. 3blue1brown and 'professor Leonard's ' series on calculus are far and away the best teaching resource available online, in my opinion. Thanks again.

  • @lokeshjadoun7624
    @lokeshjadoun7624 4 года назад

    In same question when we take a=1 then we start 'n' from 1 not from 0 why???

  • @timothymotilal6320
    @timothymotilal6320 Год назад

    thank you sir !

  • @matthewvicendese1896
    @matthewvicendese1896 7 лет назад

    wouldn't it be better to expand from 1 for obvious reasons?

  • @FrankStranathan-qj6et
    @FrankStranathan-qj6et Год назад

    What happened to the factorial in the denominator? It looks like it became n somehow?

  • @kennybyrne8778
    @kennybyrne8778 4 года назад

    what happened to the factorials?

  • @luiscardenas6339
    @luiscardenas6339 7 лет назад

    how to find the 3nd degree of these function xlnx centered at a=1 anyone

  • @danielgreeff7903
    @danielgreeff7903 8 месяцев назад +1

    untold hero

  • @albertovalsania8656
    @albertovalsania8656 4 года назад +1

    And the PEANO' REST ?

  • @ajsolis2910
    @ajsolis2910 4 года назад

    Thank you

  • @thuyoanthiphuong9260
    @thuyoanthiphuong9260 4 года назад +1

    Done
    Tks u

  • @thomasblackwell9507
    @thomasblackwell9507 5 лет назад

    sir;
    Have you become a beatnik? Man the ‘stache and van dyke do become you. Keep it up. However, you need a black beret to go with it. Love the math!

  • @pitube01
    @pitube01 4 года назад

    Why do we have a condition 0 < x

    • @carultch
      @carultch 10 месяцев назад

      It's called the radius of convergence. It can't converge any farther from the center point (x=a) to the vertical asymptote, on the left of the center point, since there's a discontinuity where it loses all differentiability at the vertical asymptote. From the name "radius of convergence", this implies that the maximum distance on the other side where it converges, it is equal to the radius of convergence. You can prove the radius of convergence works on the right of x=a, with the ratio test for series convergence. Try the ratio test at x=2.01*a, and you'll see that it diverges.

  • @hortclass4440
    @hortclass4440 5 лет назад

    Thanks man

  • @soothinggentlelightmellowr9281
    @soothinggentlelightmellowr9281 Год назад +1

    What is Taylor series for ln(abs(x)) centered at -1 ?

    • @carultch
      @carultch 10 месяцев назад +1

      Very similar to what it is, when centered at +1, which is the most common example you can look up. You just negate all the odd-ordered terms, to reflect it around the vertical axis.

  • @mytimebe5449
    @mytimebe5449 4 года назад

    thank you

  • @deepakjindal9874
    @deepakjindal9874 6 лет назад

    Pls Find the points where e^x = tanx

  • @fahad_hassan_92
    @fahad_hassan_92 Год назад

    It is probably a stupid question but, isn't Taylor series used for estimations? This expansion just chucks out ln2 + a summation in which if you put x = 2, your whole expression gives you ln2. What is the use of this?

    • @carultch
      @carultch 10 месяцев назад +1

      There are some functions where Taylor series have practical applications, like evaluating the erf(x) function. For most functions, there are other series that are much more computationally efficient to evaluate. The main purpose of Taylor series is to give an introductory idea to the concept of using infinite series to approximate transcendental functions, reducing their calculations to just arithmetic and powers, which can be calculated and integrated a lot easier. Taylor series is the easiest infinite series to introduce.

  • @TheONEDAY86
    @TheONEDAY86 5 лет назад

    hello, -1^0power is 1? so any negative number to 0 power gives 1? thank you.

    • @user-nx8fg9ny8i
      @user-nx8fg9ny8i 5 лет назад +2

      TheHouse any number,even complex number, to the zero power is one (only 0^0 is indefined)

    • @carultch
      @carultch 10 месяцев назад

      You have to snare the (-1), but yes, (-1)^0 is equal to 1. It's everywhere other than 0^0 that is equal to 1.

  • @shelbyhosey9374
    @shelbyhosey9374 2 года назад

    Solemn explanation for javascript tyranny?

  • @Bedoroski
    @Bedoroski 2 месяца назад

    Actually, the ratio test alone would make r=infinity

  • @SunilKumar-yn3md
    @SunilKumar-yn3md 4 года назад

    Please tell me sir summation(£)
    £lnx from x=0 to x = infinity
    It's value

    • @carultch
      @carultch 10 месяцев назад

      It diverges, since the sequence diverges.

  • @juice787
    @juice787 3 месяца назад

    i almost paid a guy 100$ FOR HIM TO EXPLAIN THIS TO ME thx for saving my grades and pockets

  • @IbytheGOAT
    @IbytheGOAT 3 года назад

    i love u

  • @outthewindow8188
    @outthewindow8188 5 лет назад +1

    where did the 2 and 6 in 2[2]^-3/3! and 6[2]^-4/4! go?

    • @ianvideos3149
      @ianvideos3149 5 лет назад

      It is simplified with the 3! and 4! such that only 3&4 remain at the denominator. It took a while for me to realize that lol

    • @outthewindow8188
      @outthewindow8188 5 лет назад +1

      @@ianvideos3149 thanks

  • @AnkitaKumari-eb8hq
    @AnkitaKumari-eb8hq 3 месяца назад

    i m from india and i must say it was helpful

  • @shrey245
    @shrey245 Год назад

    goat

  • @geogaddi84
    @geogaddi84 4 года назад

    Aaahh! My name is Adam and I just happened upon this. I feel special! But i'm not........

  • @geometrydashbayve5004
    @geometrydashbayve5004 6 лет назад +3

    Wait... isn't this completely pointless because ln 2 is in the actual series?

    • @nathandaniel5451
      @nathandaniel5451 6 лет назад +1

      It's a constant, so it still very easy to work with.

    • @samirgeiger1042
      @samirgeiger1042 5 лет назад

      I think you misunderstood. Its not about finding an expression for the taylor series of ln(2) but rather about finding the taylor series of ln(x) *centered* at 2

  • @denisonmoirangthem2190
    @denisonmoirangthem2190 Год назад +1

    Instead of 2 I used 1 and got stuck 😅

  • @mihaiciorobitca5287
    @mihaiciorobitca5287 6 лет назад

    How old are you,man ?

  • @adammingelgrin5939
    @adammingelgrin5939 6 лет назад

    ..what are you say at the begining

    • @blackpenredpen
      @blackpenredpen  6 лет назад +1

      adamomo orstovyesky "Adam, this video is for you"

  • @jackearhart4265
    @jackearhart4265 5 лет назад

    dude youre funny af

  • @benYaakov
    @benYaakov 2 года назад +1

    he is so similar to tony stark

  • @josephanthonycohenbrownsto8378
    @josephanthonycohenbrownsto8378 5 лет назад

    But your series does not converge onto ln(2).

  • @gemudesakio1975
    @gemudesakio1975 5 лет назад

    i love you :v

  • @amanymarwan4318
    @amanymarwan4318 7 лет назад

    please find the taylor series for
    x^4 . e^(-2x^2) about x=1

  • @MerVenim
    @MerVenim 6 лет назад

    Bizim hoca Türkçe konuşmasına rağmen böyle anlatamıyor avvsvsgsgsgs

  • @zyro3194
    @zyro3194 6 лет назад +2

    Could i have your email

  • @azzteke
    @azzteke 3 года назад

    14 Idiots