Infinite Sequences and Series: Formulas for the Remainder Term in Taylor Series

1

  • 17
  • 0
  • 0.209
  • Reply

  • Open in the desktop app ADD TO PLAYLIST

    mes

    Published on Jun 02, 2020
    About :

    In this video I expand upon my previous video on Taylor and Maclaurin series by going over a few alternative forms of the Remainder Term. Recall that the Remainder Term is just that, a remainder term, and is what is left over when approximating a function with its Taylor series. In the previous video I showed that we can use Taylor’s Inequality to determine the remainder term, but in this video, I show that we can also use an integral form as well as a form called Lagrange’s form of the remainder term. I prove both of these forms of the remainder as well as going over some examples to compare with the previous video’s use of Taylor’s Inequality.

    The topics covered in this video are listed below with their time stamps.

    1. @ 2:36 - Recap on Taylor and Maclaurin Series
    2. @ 8:26 - Formulas for the Remainder Term in Taylor Series
    3. @ 11:32 - Theorem 1: Integral Form of the Remainder Term
      • @ 40:48 - Recap of Example 4 from Previous Video
      • @ 43:44 - Example 1: sin x
        • @ 52:24 - Absolute Value Integral Property
    4. @ 1:08:42 - Lagrange's Form of the Remainder Term
      • @ 1:13:38 - Theorem 2: Weighted Mean Value Theorem for Integrals
      • @ 1:28:20 - Theorem 3: Lagrange's Form of the Remainder Term
      • @ 1:40:36 - Example 2: sin x
      • @ 1:44:35 - Example 3: x^(1/3)

    Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIiIMceHV2_A1JziAI4A?e=E7aeMn

    View video notes on the Hive blockchain: https://peakd.com/@mes/infinite-sequences-and-series-formulas-for-the-remainder-term-in-taylor-series

    Related Videos:

    Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz

    Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more

    Infinite Series: Definition, Examples, Geometric Series, Harmonics Series, Telescoping Sum + MORE: https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more

    Infinite Sequences and Series: The Integral Test and Estimate of Sums: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-integral-test-and-estimate-of-sums

    Infinite Sequences and Series: The Comparison Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-comparison-tests

    Infinite Sequences and Series: Alternating Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests

    Infinite Sequences and Series: Absolute Convergence and the Ratio/Root Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests

    Infinite Sequences and Series: Strategy for Testing Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series

    Infinite Sequences and Series: Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-power-series

    Infinite Sequences and Series: Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series

    Infinite Sequences and Series: Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series .


    SUBSCRIBE via EMAIL: https://mes.fm/subscribe

    DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

    Like, Subscribe, Favorite, and Comment Below!

    Follow us on:

    Official Website: https://MES.fm
    Hive: https://peakd.com/@mes
    Gab: https://gab.ai/matheasysolutions
    Minds: https://minds.com/matheasysolutions
    Twitter: https://twitter.com/MathEasySolns
    Facebook: https://fb.com/MathEasySolutions
    LinkedIn: https://mes.fm/linkedin
    Pinterest: https://pinterest.com/MathEasySolns
    Instagram: https://instagram.com/MathEasySolutions
    Email me: contact@mes.fm

    Try our Free Calculators: https://mes.fm/calculators

    BMI Calculator: https://bmicalculator.mes.fm
    Grade Calculator: https://gradecalculator.mes.fm
    Mortgage Calculator: https://mortgagecalculator.mes.fm
    Percentage Calculator: https://percentagecalculator.mes.fm

    Try our Free Online Tools: https://mes.fm/tools

    iPhone and Android Apps: https://mes.fm/mobile-apps

    Tags :

    mathematics calculus science messcience math

    Woo! This creator can upvote comments using 3speak's stake today because they are a top performing creator! Leave a quality comment relating to their content and you could receive an upvote worth at least a dollar.

    Their limit for today is $0!
    Comments:
    Time until mes can give away $0 to their commenters.
    0 Days 0 Hours 0 Minutes 0 Seconds
    Reply:

    To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

    More Videos

    19:03
    18 views a year ago $
    17:09
    15 views a year ago $
    02:04:05
    8 views a year ago $
    10:27
    6 views 2 months ago $