Math Easy Solutions

Exercise 3: Convergent Sequence inside a Continuous Function

Listen Later

In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). I prove this using the precise definition of limits of general functions and sequences. This theorem is also expected since a function at a particular value is equal to the limit as x approaches that particular value; thus we are just replacing the x term with the infinite sequence.

#math #sequences #limits #education #calculus

Timestamps:

  • Exercise 3: Theorem 3: Sequence inside a function: 0:00
  • Solution using the precise definition of limits: 1:27
  • f is continuous at L so limit is same as plugging in function: 3:45
  • Replace precise definition of a limit for a continuous function with the sequence: 5:54
  • Precise definition of the limit is the same for our sequence: 7:29

    • Notes and playlists:

    • Summary: https://inleo.io/threads/view/mes/re-leothreads-2q1z3cwmj
    • Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
    • Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
    • Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

      • Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

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

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

      MES Links: https://mes.fm/links

      MES Truth: https://mes.fm/truth

      Official Website: https://MES.fm
      Hive: https://peakd.com/@mes

      Email me: [email protected]

      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

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

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

      ...more
      View all episodesView all episodes
      Download on the App Store
      Math Easy SolutionsBy Math Easy Solutions